Consider a 4-product brewery problem: maximize 6L + 5D + 3A + 7P subject to malt) L

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Question:

Consider a 4-product brewery problem:

maximize 6L + 5D + 3A + 7P

subject to

malt) L + D <= 50

hops) 2L + D + 2A + P <= 150

yeast) L + D + A + 4P <= 80

where L, D, A, and P respectively represent the number of production runs of lager, dark, ale, and premium beer. The objective function seeks to maximize profit from each type of beer we might brew. The constraints on malt, hops, and yeast are in terms of pounds of each ingredient available. Given that all assumptions required for a linear programming model in terms of profit and ingredients are valid, the following optimal solution is found:

OBJECTIVE FUNCTION VALUE

1) 382.8571

VARIABLE VALUE REDUCED COST

L 50.000000 0.000000

D 0.000000 0.285714

A 24.285715 0.000000

P 1.428571 0.000000

ROW SLACK OR SURPLUS DUAL PRICES

MALT) 0.000000 3.000000

HOPS) 0.000000 0.714286

YEAST) 0.000000 1.571429

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE CURRENT ALLOWABLE ALLOWABLE

COEF INCREASE DECREASE

L 6.000000 INFINITY 0.285714

D 5.000000 0.285714 INFINITY

A 3.000000 0.500000 1.250000

P 7.000000 5.000000 2.000000

RIGHTHAND SIDE RANGES

ROW CURRENT ALLOWABLE ALLOWABLE

RHS INCREASE DECREASE

MALT 50.000000 24.285715 50.000000

HOPS 150.000000 10.000000 42.500000

YEAST 80.000000 170.000000 5.000000

a. What is the optimal choice of products and how much profit should we obtain at optimality?

b. Without re-solving (use sensitivity analysis), what is the effect on the optimal solution if I require one production run of dark beer?

c. Twenty (20) additional pounds of malt can be made available. Without re-solving (use sensitivity analysis), what is the effect on the optimal solution

d. There is some questions about the amount of profit per production run for lager and premium. How sensitive is the solution to a change in the expected profit for one or the other of these two products (examining them one at a time)? Do not resolve, use the LINDO output provided to answer this question.