MeanBeats is a company that manufactures and sells electronic musical equipment. Their headphone product line consists of two products, Reverbia and Bscape. MeanBeats sells the headphones to retailers at $600 and $300 per pack for Reverbia and Bscape, respectively. The company needs to know how many packs of each headphone to make to maximize potential revenue. They know that there will be at least twice as many Bscape orders as there are for Reverbia. Additionally, below are business rules that the company must follow on ordering packs of headphones:
i) the Bscape orders plus twice the Reverbia orders cannot exceed 20 packs.
ii) the Reverbia orders are no more than 10 more than the Bscape orders, and
iii) the Bscape orders are no more than 3 more than the Reverbia orders.
a. Formulate a linear programming model (that is, define the variables, and write down the objective function and all constraints mathematically).
b. Solve this problem using graphical analysis. Please label each constraint and identify the feasible region on the graph. Plot several level curves of the objective function line and clearly identify the optimal point.
c. What is the optimal solution? What is the optimal value?
d. Explain in words what will be your recommendations to your company based on the solution of the optimization problem.