The formulas below are the cost and revenue functions for th

The formulas below are the cost and revenue functions for the company that manufactures and sells small radius. Use the formula shown to write the company\'s profit function , p from producing and selling radius find the company\'s profit if 25000 radius are produced and sold C(x) * 80000 + 44x and R(x) = 49x The company\'s profit function is P(x) = (simplyfy your answer) The company\'s profit from selling 25000 redius is $ (simplyfy your answer)

Solution

Given : C(x) = 80,000 + 44x

R(x) = 49x

We know that:

Profit = Revenue - Cost

Profit P(x) = (49x) - (80,000 + 44x)

Profit P(x) = 49x - 80000 - 44x

Profit P(x) = 5x - 80000

(b),

if 25000 radios are sold,

then, plug x = 25000, we get:

Profit = 5*(25000) - 80000

         = 125000 - 80000

Profit = $ 45,000

Since the profit is zero at the break-even point

0 = 5x - 80000

80000 = 5x

x = 16,000 units.

Once they sell 16,000 units, any units sold afterwards shows a profit.