Problem 8-23 Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Grinder Shaper Component 1 6 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. a. Formulate and solve for the recommended production quantities. Let C1 = units of component 1 manufactured C2 = units of component 2 manufactured C3 = units of component 3 manufactured Max 8 C1 + 6 C2 + 9 C3 s.t 601 + 4 C2 + 4 C3s 7200 Constraint 1 4 C1 + 5 C2 + 2C3 s 6600 Constraint 2 1 C35 200 Iconstraint 3 1 C1 1000 Constraint 4 The optimal solution is C1 = 600 C2l= 700 200 b. What are the objective coefficient ranges for the three components? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to two decimal places. Objective Coefficient Range Variable lower limit upper limit C1 NA 9 C2 5.33 9 C3 6 NA Interpret the above ranges for company management. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Individual changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce. c. What are the right-hand-side ranges? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to two decimal places, Right-Hand-Side-Range Constraints lower limit upper limit 1 4400 7400 x 2 6000 X NA 3 NA 200 x 4 600 600 X 5 NA 700 X 6 60000 NA X Interpret the above ranges for company management. The input in the box below will not be graded, but may be reviewed and considered by your instructor. d. If more time could be made available on the grinder, how much would it be worth? 300 x Problem 8-23 Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Grinder Shaper Component 1 6 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. a. Formulate and solve for the recommended production quantities. Let C1 = units of component 1 manufactured C2 = units of component 2 manufactured C3 = units of component 3 manufactured Max 8 C1 + 6 C2 + 9 C3 s.t 601 + 4 C2 + 4 C3s 7200 Constraint 1 4 C1 + 5 C2 + 2C3 s 6600 Constraint 2 1 C35 200 Iconstraint 3 1 C1 1000 Constraint 4 The optimal solution is C1 = 600 C2l= 700 200 b. What are the objective coefficient ranges for the three components? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to two decimal places. Objective Coefficient Range Variable lower limit upper limit C1 NA 9 C2 5.33 9 C3 6 NA Interpret the above ranges for company management. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Individual changes in the profit coefficients within these ranges will not cause a change in the optimal number of components to produce. c. What are the right-hand-side ranges? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to two decimal places, Right-Hand-Side-Range Constraints lower limit upper limit 1 4400 7400 x 2 6000 X NA 3 NA 200 x 4 600 600 X 5 NA 700 X 6 60000 NA X Interpret the above ranges for company management. The input in the box below will not be graded, but may be reviewed and considered by your instructor. d. If more time could be made available on the grinder, how much would it be worth? 300 x
