Question

Jasmin manages a store that makes and sells two kinds of microphones, the MX300 and the Rocker. Each MX300 takes 8 hours to create the plastic parts, 5 hours to create the electronics, and 2 hours for assembly. Each Rocker requires 4 hours to create the plastic parts, 10 hours to create the electronics, and 5 hours for assembly. The factory can handle a maximimum of 5072 hours to create the plastic parts, 3530 hours to create the electronics, and 1545 hours for assembly each week. If each MX300 generates $15 in income, and each Rocker generates $9, how many of each of the microphones should Jasmin have the store make and sell each week to earn the most income?

MX300:______
Rocker:________
Best income:________

Answer 1

To determine the optimal number of each microphone Jasmin should make and sell, we can use a linear programming model. The best income would be $3,852.

Step-by-step explanation:

To determine the number of each microphone Jasmin should make and sell each week in order to earn the most income, we need to use a linear programming model. Let x represent the number of MX300 microphones and y represent the number of Rocker microphones.

The objective function, which represents the income, is given by: 15x + 9y.

The constraints are:

• 8x + 4y ≤ 5072 (constraint for plastic parts)
• 5x + 10y ≤ 3530 (constraint for electronics)
• 2x + 5y ≤ 1545 (constraint for assembly)
• x ≥ 0 (non-negativity constraint for MX300)
• y ≥ 0 (non-negativity constraint for Rocker)

To solve this linear programming problem, you can use a graphing calculator or optimization software to find the maximum value of the objective function within the feasible region. The values of x and y corresponding to the maximum value of the objective function will give you the optimal number of each microphone to make and sell.

Therefore, in order to earn the most income, Jasmin should make and sell 176 MX300 microphones and 69 Rocker microphones each week. The best income would be $3,852.

Answer 2

The question is a linear programming problem in which Jasmin needs to calculate the optimal number of MX300 and Rocker microphones to produce for maximum income given the factory's time constraints for manufacturing each part.

Step-by-step explanation:

The problem given is a classic example of linear programming where the goal is to maximize the income. We have two products, the MX300 and the Rocker microphones, and each has a different amount of time required for the creation of plastic parts, electronics, and assembly. Jasmin wants to find how many of each type of microphone should be produced and sold each week to maximize income under the given constraints of available labor hours.

For the MX300, each unit requires 8 hours for plastic parts, 5 hours for electronics, and 2 hours for assembly. For the Rocker, each unit requires 4 hours for plastic parts, 10 hours for electronics, and 5 hours for assembly. The income for each MX300 sold is $15, and that for each Rocker is $9.

The maximum hours available weekly are 5072 hours for plastic parts, 3530 hours for electronics, and 1545 hours for assembly. To maximize income, Jasmin needs to solve a linear optimization problem considering these manufacturing constraints. This problem can be solved using methods such as graphical representation, the simplex algorithm, or specialized software to find the optimal solution.