A merchant plans to sell two models of home computers at costs of $250 and $400, respectively. The $250 model yields a profit of $45 and the $400 model yields a profit of $50. The merchant estimates that the total monthly demand will not exceed 250 units. Find the number of units of each model that should be stocked in order to maximize profit. Assume that the merchant does not want to invest more than $70,000 in computer inventory. (See Exercise 21 in Section 9.2.)

That is there is maximum profit when 250 units of $250 model computer and 50 units of $400 model computer is stocked.

Explanation:

Let x represent the number of $250 model and let y represent the number of $400 model. Since the total monthly demand will not exceed 250 units, hence:

x + y < 250      (1)

Also the merchant does not want to invest more than $70,000, hence:

250x + 400y < 70000     (2)

x, y ≥ 0

Plotting the equations using geogebra online graphing tool. The solution to the problem is at (0,0), (200, 50), (250,0), (0, 175).

The profit equation is:

Profit = 45x + 50y

At (0,0); Profit = 45(0) + 50(0) = 0

At (250,0); Profit = 45(250) + 50(0) = $11250

At (0,175); Profit = 45(0) + 50(175) = 8750

At (200,50); Profit = 45(200) + 50(50) = $11500

Therefore the maximum profit is at (200, 50). That is there is maximum profit when 250 units of $250 model computer and 50 units of $400 model computer is stocked.

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