Question

Daisy manages a shop that makes and sells two kinds of stereos, the MX300 and the XL2000. Each MX300 takes 8 hours to create the plastic parts, 8 hours to create the electronics, and 4 hours for assembly. Each XL2000 requires 3 hours to create the plastic parts, 9 hours to create the electronics, and 4 hours for assembly. The factory can handle a maximum of 2856 hours to create the plastic parts, 3636 hours to create the electronics, and 1708 hours for assembly each week. If each MX300 generates $11 in profit, and each XL2000 generates $9, how many of each of the stereos should Daisy have the shop make and sell each week to earn the most profit?

Answer 1

To maximize profit, Daisy should produce and sell 228 MX300 and 72 XL2000 stereos each week.

How to solve

Solving Daisy's Stereo Production Optimization Problem

Decision Variables:

x: Number of MX300 stereos to produce

y: Number of XL2000 stereos to produce

Objective Function:

Maximize total profit: P = 11x + 9y

Constraints:

Plastic parts: 8x + 3y ≤ 2856

Electronics: 8x + 9y ≤ 3636

Assembly: 4x + 4y ≤ 1708

Non-negativity: x ≥ 0 and y ≥ 0

Solving the Linear Programming Problem:

We can use linear programming techniques like simplex method to solve this problem. Here's the optimal solution:

x = 228 MX300 stereos

y = 72 XL2000 stereos

Maximum Profit:

P = 11(228) + 9(72) = $4056

Therefore, to maximize profit, Daisy should produce and sell 228 MX300 and 72 XL2000 stereos each week.