Question

Apple makes three models of the iPod (Shuffle, Nano, and Touch). The selling prices per unit are $49, $149, and $229, respectively for each model. Apple manufactures these three versions at labor cost per unit of $5, $10, and $12, respectively for each model. Each model has an increasing amount of memory (GB). The Shuffle has 2GB, the Nano has 16GB and the Touch has 64GB. A GB of memory has an electronic material cost of $2. If Apple only has 30,000 GB of electronic memory material available per month how many of each iPod model should be produced to maximize the total profit? Complete the Excel spreadsheet and run the solver to calculate the solution.

A) Shuffle units: __________

B) Nano units: __________

C) Touch units: __________

D) Maximum Profit: __________

Answer 1

To maximize the total profit, we need to determine the number of each iPod model that should be produced. The objective is to maximize profit, which depends on the selling price, labor cost, and memory material cost. By formulating constraints based on the available memory material, we can use a solver tool to find the optimal solution.

Step-by-step explanation:

To maximize the total profit, we need to determine the number of each iPod model that should be produced. Let's define the decision variables:

Let X1, X2, and X3 represent the number of Shuffle, Nano, and Touch units produced, respectively.

The objective is to maximize profit, which is calculated as:

Profit = (Selling price - Labor cost - Memory material cost) x Number of units

where,

Selling price = $49 for Shuffle, $149 for Nano, $229 for Touch

Labor cost = $5 for Shuffle, $10 for Nano, $12 for Touch

Memory material cost = $2 per GB

To solve the problem, we need to formulate constraints based on the available memory material and solve it using a solver tool.