J. Outdoors, Inc. has, as one of its product lines, lawn furniture. They currently have three items in that line: a lawn chair, a standard bench, and a table. These products are produced in a two-step manufacturing process involving the tube-bending department and the welding department. The time required by each item in each department is as follows: Tube bending Welding Lawn chair 1.2 0.8 Product Bench 1.7 0 Table 23 12 1.2 2.3 Present capacity 1000 1200 The contribution that Outdoors, Inc. receives from the manufacture and sale of one unit of each product is $3 for a chair, $3 for a bench, and $5 for a table. The company is trying to plan its production mix for the current selling season. It predicts that it can sell any number it produces, but production is further limited by available material, because of a prolonged strike. The company currently has on hands 2000 lbs. of tubing. The three products require the following amounts of this tubing: 2 lbs. per chair, 3 lbs. per bench, and 4.5 lbs, per table. In order to determine the optimal product mix, the production manager has formulated the following linear program: Label Bending Welding Material Availability Contribution 3 Variable Cells Constraints Chair 1.2 0.8 2 28 Cell Name $B$6 Chair Bench 1.7 0 3 Objective Cell (Max) Cell Name $G$7 Final Value 700 3 $C$6 Bench 0 $D$6 Table 133.3333333 Final Table Reduced Cost 0 7124 1.383333333 0 235 Solving this linear program with Excel and asking for a sensitivity report on the solution yields the information: 2.3 4.5 5 S 3 S Original Value Final Value 2,766.666667 2,766.666667 5 Limit 1,000 1,200 2,000 Objective Allowable Coefficient Increase 3 2 1.383333333 1.75 Shadow Constraint Allowable Allowable Decrease 0.777777778 1E+30 2 Allowable Cell Name $G$2 s $G$3 s $G$4 s Value 1000 866.6666667 2000 Price 1.166666667 0 0.8 R.H. Side 1000 1200 2000 Decrease 466.6666667 1E+30 333.3333333 555.5555556 333.3333333 Increase N 200 What is the optimal production mix? What contribution can the firm anticipate by producing this mix? (b) What is the value of one more unit of tube-bending time? of welding time? of metal tubing? Please, justify your answer. (c) A local distributor has offered to sell Outdoors, Inc. some additional metal tubing for $0.70/lb. Should Outdoors buy it? If yes, how much would the firm's contribution increase if they bought 550 lbs. and used it in an optimal fashion?