Question

A store plans to sell two different game consoles, the YuuMi and the ZBox. The store’s wholesale cost for a YuuMi is $250, and the store can sell one for $295. The ZBox’s wholesale price is $400, and the store can sell it for $450. The store’s marketing research indicates that the total monthly demand for game consoles will not exceed 250 units sold. The store’s financial manager does not want to invest more than $70,000 in inventory costs for game consoles. How many of each game console should the store stock in order to maximize their profits, and what is their maximum monthly profit?
Constraints:

Objective formula:

Answer 1

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Answer:

• Constraints: x + y ≤ 250; 250x +400y ≤ 70000; x ≥ 0; y ≥ 0
• Objective formula: p = 45x +50y
• 200 YuuMi and 50 ZBox should be stocked
• maximum profit is $11,500

Step-by-step explanation:

Let x and y represent the numbers of YuuMi and ZBox consoles, respectively. The inventory cost must be at most 70,000, so that constraint is ...

  250x +400y ≤ 70000

The number sold will be at most 250 units, so that constraint is ...

  x + y ≤ 250

Additionally, we require x ≥ 0 and y ≥ 0.

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A profit of 295-250 = 45 is made on each YuuMi, and a profit of 450-400 = 50 is made on each ZBox. So, if we want to maximize profit, our objective function is ...

  profit = 45x +50y

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A graph is shown in the attachment. The vertex of the feasible region that maximizes profit is (x, y) = (200, 50).

200 YuuMi and 50 ZBox consoles should be stocked to maximize profit. The maximum monthly profit is $11,500.