Question

The profit made by a company when 60 units of its product is sold is $1600. When 150 units of its products are sold, the profit increases to $5200. Assuming that the profit function is linear and of the form

Answer 1

Answer to Question #87538 – Math – Algebra

Question

The profit made by a company when 60 units of its product is sold is $1600. When 150 units of its products are sold, the profit increases to $5200. Assuming that the profit function is linear and of the form.

Solution

Let profit function be linear as follows:

$$P(u) = a + bu$$

When $u = 60, P = 1600$

$$1600 = a + 60b \quad \dots \dots (i)$$

When $u = 150, P = 5200$

$$5200 = a + 150b \quad \dots \dots (ii)$$

Subtracting (i) from (ii),

$$5200 = a + 150b$$ $$1600 = a + 60b$$ $$- \quad - \quad -$$ $$3600 = 90b$$ $$b = \frac{3600}{90}$$ $$b = 40.$$

Put this value in (i),

$$1600 = a + 60(40)$$ $$1600 = a + 2400$$ $$a = -800.$$

So, Profit function: $P(u) = 40u - 800$.

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