Gatson Manufacturing Company Is Willing to Promote 2 Types of Tires

Essay

Gatson manufacturing company is willing to promote 2 types of tires: Economy tire; Premium tire, and these two tires are independent of each other in terms of demand, cost, price, etc. An analytics team of this company has estimated the profit functions for both the tires as,
Monthly profit for Economy tire = 49.2415 LN(XA) + 180.414
Monthly profit for Premium tire = 84.344 LN(XB) - 150.112
where XA and XB are the advertising amount allocated to Economy tire and Premium tire, respectively, and LN is the natural logarithm function. The advertising budget is $200,000, and management has dictated that at least $20,000 must be allocated to each of the two tires.
(Hint: To compute a natural logarithm for the value X in Excel, use the formula =LN(X). For Solver to find an answer, you also need to start with decision variable values greater than 0 in this problem.)
Develop and solve an optimization model that will prescribe how the company should allocate its marketing budget to maximize profit.