you own a pizza restaurant the selling price is $12 for each pizza the cost to make each pizza is $5 you have a fixed labor cost of $230 and you sell 85 pizzas what is your profit? How many pizzas would need to be sold to make a profit of $700? How many pizzas would need to be sold if you wanted to make a profit greater than $1,000?

Recall: **Profit = Revenue - Cost**

**P(x) = R(x) - C(x) ** , where **
x** is the *number of pizzas sold*

**Revenue**, **R(x)**, is given by the following:

**R(x) = (selling price)·(# of pizzas sold) **

** R(x) = 12x**

**Cost**, **C(x)**, is given by the following:

**C(x) = (variable cost)·(# of pizzas sold) + fixed cost**

** C(x) = 5x + 230**

Therefore, since Profit = Revenue - Cost

**P(x) = R(x) - C(x)**

P(x) = 12x - (5x + 230)

P(x) = 12x - 5x - 230

**P(x) = 7x - 230**

Thus, the *profit of selling 85 pizzas is determined by solving P(x) when x=85*:

P(x) = 7x - 230

**P(85)** = 7(85) - 230

= 595 - 230

**= 365**

Since P(85) = 365 , *selling 85 pizzas yield a profit of $365*.

To find *how many pizzas need to be sold to yield a profit of $700*, *
solve for x when P(x)=700*:

P(x) = 7x - 230

**700** = 7x - 230

700 + 230 = 7x - 230 + 230

930 = 7x

930/7 = 7x/7

**132.86 = x**

** x ≈ 133**

Thus, *to make a profit of $700*, * 133 pizzas need to be sold*.

To find *how many pizzas need to be sold to yield a profit greater than $1000*,
* solve for x when P(x)>1000*:

P(x) = 7x - 230

**7x - 230 > 1000**

7x - 230 + 230 > 1000 + 230

7x > 1230

7x/7 > 1230/7

** x > 175.7**

** x ≥ 176**

Thus, *to make a profit greater than $1000*, *you would need to sell at least
176 pizzas*.