Question

the cost in dollars to produce x t-shirts is $c(x)=3.07x + 90$. the revenue in dollars from sales of x t-shirts is $r(x)=11.83x$.
(a) write and simplify a function p that gives profit in terms of x.
(b) find the profit if 70 t-shirts are produced and sold.

(a) $p(x) = \square$
(use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Define profit function

Profit = Revenue - Cost, so $P(x) = R(x) - C(x)$

Step2: Substitute given functions

$P(x) = 11.83x - (3.07x + 90)$

Step3: Simplify the expression

$P(x) = 11.83x - 3.07x - 90 = 8.76x - 90$

Step4: Substitute x=70 into P(x)

$P(70) = 8.76 \times 70 - 90$

Step5: Calculate the final value

$P(70) = 613.2 - 90 = 523.2$

Answer:

(a) $P(x) = 8.76x - 90$
(b) $\$523.20$