Chapter 2.1, Problem 104AYU

To determine

To find: The revenue $R$, in dollars, from selling $x$ clocks, is $R\left(x\right)=30x$ and the cost $C$, in dollars, of selling $x$ clocks, is $C\left(x\right)=0.1x²+7x + 400$ then find

1. The profit function $P\left(x\right) = R\left(x\right) - C\left(x\right)$
2. The profit if $x = 30$ hundred clocks are sold.
3. Interpret $P\left(30\right)$

Answer to Problem 104AYU

a) $P\left(x\right)= -0.1x²+23x - 400$; b) $\$200$; c) The profit is $\$200$ when 30 clocks are sold.

Explanation of Solution

Given:

The revenue $R$, in dollars, from selling $x$ clocks, is $R\left(x\right)=30x$ and the cost $C$, in dollars, of selling $x$ clocks, is $C\left(x\right)=0.1x²+7x + 400$

Calculation:

a) the stopping distance function $P\left(x\right) = R\left(x\right) - C\left(x\right)$

$P\left(x\right)=30x - \left(0.1x²+7x + 400\right)$

$=- 0.1x²+\left(30-7\right)x - 400$

$= -0.1x²+23x - 400$

b) $P\left(30\right) = -0.1\left(30\right)²+23\left(30\right)-400$

$= -0.1\left(900\right)+23\left(30\right)-400$

$= -90+690 -400$

$= 690-490$

$=\$200$

c) The profit is $\$200$ when 30 clocks are sold.