The Pitts Barbecue Company makes three kinds of barbecue sauce: Extra Hot, Hot,
and Mild. Pitts’ vice president of marketing estimates that the company can sell 8,000
cases of its Extra Hot sauce plus 10 extra cases for every dollar it spends promoting
this sauce; 10,000 cases of Hot sauce plus 8 extra cases for every dollar spent promoting
this sauce; and 12,000 cases of its Mild sauce plus 5 extra cases for every dollar
spent promoting this sauce. Although each barbecue sauce sells for $10 per case, the
cost of producing the different types of sauce varies. It costs the company $6 to produce
a case of Extra Hot sauce, $5.50 to produce a case of Hot sauce, and $5.25 to produce
a case of Mild sauce. The president of the company wants to make sure the company
manufactures at least the minimum amounts of each sauce that the marketing
vice president thinks the company can sell. A budget of $25,000 total has been approved
for promoting these items of which at least $5,000 must be spent advertising
each item. How many cases of each type of sauce should be made, and how do you
suggest that the company allocate the promotional budget to maximize profits?
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?