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.