Question

If

Answer 1

The profit is maximized when approximately 517 units is produced.

What is a profit function?

A profit function is the difference between revenue and cost.

The given cost function is presented as follows;

C(x) = 1200 + 500•x - 2.6•x² + 0.04•x³

The demand function is presented as follows;

p(x) = 1700 - 8•x

Required;

The production level that will maximize profitm.

Solution;

From the demand function, we have;

The price = x

Therefore;

Revenue, R(x) = x × (1700 - 8•x) = 1700•x - 8•x²

Therefore;

Profit = R(x) - C(x)

Which gives;

Profit = 1700•x - 8•x² - (1200 + 500•x - 2.6•x² + 0.04•x³) = -0.04•x³+5.4•x²-750•x+750

At maximum profit, we have;

• Profit' = -3•x²-135.2•x +3000 = 0

Which gives;

x ≈ 64.66

Therefore;

The quantity that gives the most profit is as follows;

P(x) ≈ 1700 - 64.66×8 ≈ 517.28

The production level that will maximize profit is therefore approximately 517 units

Learn more about the profit function here:

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