Question

Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 300. Its cost (in dollars) for a run of x hockey jerseys is
C(x) = 3000 + 10x + 0.2x2 (0 ≤ x ≤ 300)
Gymnast Clothing sells the jerseys at $110 each. Find the revenue function.
R(x) =


Find the profit function.
P(x) =


How many should Gymnast Clothing manufacture to make a profit? HINT [See Example 2.] (Round your answer up to the nearest whole number.)

Answer 1

Given that Gymnast Clothing sells the jerseys at $110 each, the revenue function is given by

$R(x)=110x$

Profit function is given by revenue function minus cost function, i.e.

$P(x)=R(x)-C(x)=110x-(3000+10x+0.2x^2)=110x-3000-10x-0.2x^2=-0.2x^2+100x-3000$

Thus,
$P(x)=-0.2x^2+100x-3000$

The number Gymnast Clothing should manufacture to make a profit is given by
$-0.2x^2+100x-3000=0 \\ \\ \Rightarrow0.2x^2-100x+3,000=0 \\ \\ \Rightarrow x=468, \ 32$

Because, Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 300.

The number Gymnast Clothing should manufacture to make a profit is 32.