Sugarco can manufacture three types of candy bar. Each candy bar consists totally of sugar and chocolate. The compositions of each type of candy bar and the profit earned from each candy bar are shown in the table below.
Fifty oz. of sugar and 100 oz. of chocolate are available. After defining xi to be the number of type I
candy bars manufactured, Sugarco should solve the following LP:
After adding slack variables s1 and s2, the optimal tableau is as shown below.
Using this optimal tableau, answer the following.
a) For what values of type 1 candy bar profit does the current basis remain optimal? If the profit for a type 1 candy bar profit were 7 cents, what would be the new optimal solution to Sugarco’s problem?
b) For what values of type 2 candy bar profit would the current basis remain optimal? If the profit for a type 2 candy bar were 13 cents, then what would be the new optimal solution to Sugarco’s problem?
c) For what amount of available sugar would the current basis remain optimal?
d) If 60 oz. of sugar were available, what would be the Sugarco’s profit? How many of each candy bar should the company make? Could these questions be answered if only 30 oz. of sugar were available?
e) Suppose a Type 1 candy bar used only 0.5 oz. of sugar and 0.5 oz. of chocolate. Should Sugarco now make type 1 candy bars?
f) Sugarco is considering making type 4 candy bars. A type 4 candy bar earns 17 cents profit and requires 3 oz. of sugar and 4 oz. of chocolate. Should Sugarco produce any type 4 candy bars?
