Question: Problem 1) Par Golf, Inc. makes three types of golf balls, Pro, Regular, and Discount. The daily input of the principal raw material, syrlyn, is
Problem 1) Par Golf, Inc. makes three types of golf balls, Pro, Regular, and Discount. The daily input of the principal raw material, syrlyn, is 45 canisters and there are 12 hours available on the molding machines. Each case of Pro balls requires the equivalent of 4 canisters of syrlyn, Regular balls require 2.5 canisters and Discount balls require 1.8 canisters per case. Each case of balls, regardless of type, requires one hour on the molding machines. Marketing cannot sell more than 12 cases of Pro balls and no more than 14 of the Regular balls. Let P, R and D be the cases of Pro, Regular, and Discount balls to be manufactured per day. The objective function reflects expected daily profit. Par Golf, Inc. should solve the following LP to find the optimal production plan: MAX 120P+100R+70D S.T. 2) 4P+2.5R+1.8D S 45 3) P+R+DS 12 4) PS 12 5) RS 14 Note that all variables are nonnegative. The problem has been solved using Lindo with the following output. Use the Lindo output to answer the following questions: OBJECTIVE FUNCTION VALUE RANGES IN WHICH THE BASIS IS UNCHANGED: 1) 1400.000 VARIABLE VALUE P 10.000000 R 2.000000 D 0.000000 REDUCED COST 0.000000 0.000000 20.666666 OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE P 120.000000 40.000000 19.999998 R 100.000000 19.999998 14.090907 D 70.000000 20.666662 INFINITY ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 13.333333 3) 0.000000 66.666664 4) 2.000000 0.000000 5) 12.000000 0.000000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 45.000000 3.000000 15.000000 3 12.000000 4.500000 0.750000 4 12.000000 INFINITY 2.000000 5 14.000000 INFINITY 12.000000 a) What is the daily profit level? Which variables are the basic variables? What are the values of those basic variables? (2 pts) b) What constraints are binding? (2 pts) c) Suppose ABC Chemical Company offers to sell Par Golf, Inc. 2 more canisters of syrlyn for $10. Should Par Golf, Inc. buy more syrlyn? Why? (2 pts) d) How much does the daily profit change if the availability of the molding machines is reduced from 12 to 11.5 hours due to scheduled maintenance? (2 pts) e) Suppose the price of a case of Pro balls is increased to $140. What will be the new optimal solution? (2 pts)
