Problem 3-06 (Algorithmic) Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 700 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (hours) Packaging and Shipping Model Finishing Profit/Glove Cutting and Sewing 1 10/ Regular model 2 $7 1/8 1/5 Catcher`s model 1. $10 /3 /3 Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 7R + 10C s.t. R+ 10/3C 700 1/2 R + 1/3C 300 1/8R+ 1/5C 100 R, C 0 The sensitivity report is shown in figure below. Cutting and sewing Finishing Packaging and shipping The sensitivity report is shown in figure below. Optimal Objective Value = 4400.00000 Variable Value R 575.00000 37.50000 Constraint Slack/Surplus 1 0.00000 2 0.00000 3 20.62500 Variable R Constraint 1 2 3 Objective Coefficient 7.00000 10.00000 RHS Value 700.00000 300.00000 100.00000 Allowable Increase 8.00000 13.33330 Allowable Increase 471.42800 50.00000 Infinite Reduced Cost Dual Value 0.00000 0.00000 2.00000 10.00000 0.00000 Allowable Decrease 4.00000 5.33330 Allowable Decrease 100.00000 230.00000 20.62500 a. Determine the objective coefficients ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Objective Coefficient Range Variable lower limit upper limit I Regular Glove Catcher's Mitt b. Interpret the ranges in part (a.). As long as the profit per regular glove is the optimal solution of gloves will not change. Or as long as the profit per catcher glove is The assumption is that the optimal solution of changed at a/the same time. gloves will not change. c. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Constraint Right-Hand-Side Range lower limit upper limit Cutting and Sewing Finishing Packaging As long as the number of hours available for cutting and sewing (Constraint 1) are As long as the number of hours available for finishing (Constraint 2) are As long as the number of hours available for packaging (Constraint 3) are d. How much will the value of the optimal solution improve if 9 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is Screenshot(Alt + A) b. Interpret the ranges in part (a.). As long as the profit per regular glove is or as long as the profit per catcher glove between $3.00 and $15.00 between $7.00 and $15.00 The assumption is that the optimal solution of he optimal solution of between $4.00 and $15.00 between $3.00 and $7.00 e time. gloves will not change. gloves will not change. b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is The assumption is that the optimal solution of the optimal solution changed at a/the same time. gloves will not change. 575 regular and 37.5 catcherves will not change. 37.5 regular and 575 catcher 4400 regular and catcher b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is the optimal solution of gloves will not change. The assumption is that between $5.33 and $23.33 he. between $4.67 and $10.00 between $10.00 and $23.33 c. Interpret the right-hand-side ranges. If ther between $4.67 and $23.33 then enter the text "NA" as your answer. Round your answers to two decimal places. the optimal solution of gloves will not change. b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is the optimal solution of gloves will not change. The assumption is that changed at a/the same time. 575 regular and 37.5 catcher 37.5 regular and 575 catcher 4400 regular and catcher c. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. the optimal solution of gloves will not change. b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is The assumption is that c. Interpret the right-handonly one variable is both variables are the optimal solution of gloves will not change. gloves will not change. the optimal solution of changed at a/the same time. is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. c. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Constraint Right-Hand-Side Range lower limit upper limit Cutting and Sewing Finishing Packaging As long as the number of hours available for cutting and sewing (Constraint 1) are As long as the number of hours available for finishing (Constraint 2) are . As long as the number of hours available for packaging (Constraint 3) are d. How much will the value of the optimal solution improve if 9 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is between 600.00 and 1171.43 between 100.00 and 1171.43 between 600.00 and 700.00 optimal value of the solution per unit increase in the right-hand side of the constraint is between 700.00 and 1171.43 the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is As long as the number of hours available for cutting and sewing (Constraint 1) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is As long as the number of hours available for finishing (Constraint 2) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is between 300.00 and 350.00 between 70.00 and 350.00 As long as the number of hours available for packaging (Constraint 3) ar between 230.00 and 350.00 change in the optimal value of the solution per unit increase in the right-hand side of the constraint is between 70.00 and 300.00 d. How much will the value of the optimal solution improve if 9 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $ As long as the number of hours available for cutting and sewing (Constraint 1) are As long as the number of hours available for finishing (Constraint 2) are As long as the number of hours available for packaging (Constraint 3) are d. How much will the value of the optimal solution improve if 9 extra hours of79.38 or above between 20.63 and 100.00 Amount: $ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is 20.63 or above between 79.38 and 100.00 me are made available? If required, round your answer to three decimal places. Problem 3-06 (Algorithmic) Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 700 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (hours) Packaging and Shipping Model Finishing Profit/Glove Cutting and Sewing 1 10/ Regular model 2 $7 1/8 1/5 Catcher`s model 1. $10 /3 /3 Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 7R + 10C s.t. R+ 10/3C 700 1/2 R + 1/3C 300 1/8R+ 1/5C 100 R, C 0 The sensitivity report is shown in figure below. Cutting and sewing Finishing Packaging and shipping The sensitivity report is shown in figure below. Optimal Objective Value = 4400.00000 Variable Value R 575.00000 37.50000 Constraint Slack/Surplus 1 0.00000 2 0.00000 3 20.62500 Variable R Constraint 1 2 3 Objective Coefficient 7.00000 10.00000 RHS Value 700.00000 300.00000 100.00000 Allowable Increase 8.00000 13.33330 Allowable Increase 471.42800 50.00000 Infinite Reduced Cost Dual Value 0.00000 0.00000 2.00000 10.00000 0.00000 Allowable Decrease 4.00000 5.33330 Allowable Decrease 100.00000 230.00000 20.62500 a. Determine the objective coefficients ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Objective Coefficient Range Variable lower limit upper limit I Regular Glove Catcher's Mitt b. Interpret the ranges in part (a.). As long as the profit per regular glove is the optimal solution of gloves will not change. Or as long as the profit per catcher glove is The assumption is that the optimal solution of changed at a/the same time. gloves will not change. c. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Constraint Right-Hand-Side Range lower limit upper limit Cutting and Sewing Finishing Packaging As long as the number of hours available for cutting and sewing (Constraint 1) are As long as the number of hours available for finishing (Constraint 2) are As long as the number of hours available for packaging (Constraint 3) are d. How much will the value of the optimal solution improve if 9 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is Screenshot(Alt + A) b. Interpret the ranges in part (a.). As long as the profit per regular glove is or as long as the profit per catcher glove between $3.00 and $15.00 between $7.00 and $15.00 The assumption is that the optimal solution of he optimal solution of between $4.00 and $15.00 between $3.00 and $7.00 e time. gloves will not change. gloves will not change. b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is The assumption is that the optimal solution of the optimal solution changed at a/the same time. gloves will not change. 575 regular and 37.5 catcherves will not change. 37.5 regular and 575 catcher 4400 regular and catcher b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is the optimal solution of gloves will not change. The assumption is that between $5.33 and $23.33 he. between $4.67 and $10.00 between $10.00 and $23.33 c. Interpret the right-hand-side ranges. If ther between $4.67 and $23.33 then enter the text "NA" as your answer. Round your answers to two decimal places. the optimal solution of gloves will not change. b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is the optimal solution of gloves will not change. The assumption is that changed at a/the same time. 575 regular and 37.5 catcher 37.5 regular and 575 catcher 4400 regular and catcher c. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. the optimal solution of gloves will not change. b. Interpret the ranges in part (a.). As long as the profit per regular glove is Or as long as the profit per catcher glove is The assumption is that c. Interpret the right-handonly one variable is both variables are the optimal solution of gloves will not change. gloves will not change. the optimal solution of changed at a/the same time. is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. c. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Constraint Right-Hand-Side Range lower limit upper limit Cutting and Sewing Finishing Packaging As long as the number of hours available for cutting and sewing (Constraint 1) are As long as the number of hours available for finishing (Constraint 2) are . As long as the number of hours available for packaging (Constraint 3) are d. How much will the value of the optimal solution improve if 9 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is between 600.00 and 1171.43 between 100.00 and 1171.43 between 600.00 and 700.00 optimal value of the solution per unit increase in the right-hand side of the constraint is between 700.00 and 1171.43 the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is As long as the number of hours available for cutting and sewing (Constraint 1) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is As long as the number of hours available for finishing (Constraint 2) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is between 300.00 and 350.00 between 70.00 and 350.00 As long as the number of hours available for packaging (Constraint 3) ar between 230.00 and 350.00 change in the optimal value of the solution per unit increase in the right-hand side of the constraint is between 70.00 and 300.00 d. How much will the value of the optimal solution improve if 9 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $ As long as the number of hours available for cutting and sewing (Constraint 1) are As long as the number of hours available for finishing (Constraint 2) are As long as the number of hours available for packaging (Constraint 3) are d. How much will the value of the optimal solution improve if 9 extra hours of79.38 or above between 20.63 and 100.00 Amount: $ the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is 20.63 or above between 79.38 and 100.00 me are made available? If required, round your answer to three decimal places