If a manufacturer charges q dollars each for footballs, then he can sell 3000-150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find the weekly revenue if the price is $8 for each football.
To find the polynomial R(q) that represents the revenue for one week, we need to multiply the number of footballs sold, 3000-150q, by the price charged for each football, q.
The revenue R(q) is given by:
R(q) = (3000 - 150q) * q
Simplifying the expression, we have:
R(q) = 3000q - 150q^2
To find the weekly revenue if the price is $8 for each football, we substitute q = 8 into the polynomial R(q):
R(8) = 3000(8) - 150(8^2)
R(8) = 24000 - 150(64)
R(8) = 24000 - 9600
R(8) = 14400
Therefore, the weekly revenue when the price is $8 for each football is $14,400.