Solve the problem.
If a manufacturer charges q dollars each for footballs, then he can sell
3000 – 150q footballs per week. Find the polynomial R(q) that represents
the revenue for one week. Find the weekly revenue if the price is $8 for each football.
I don't understand how to do this word solving problem. I need to show my work and do not understand how to do this. Please help. Thanks.
You have been told the formula for the number sold per week. Thet is the R(q0 formula. Multiply that by the price (q) to obtain the revenue (cash received) per week. It is that simple. Then substitute $8 for q to get the numerical revenue value is $8 is charged per football.
This is hardly a 'word solving' problem. It is just following directions.
To solve this problem, we need to find the polynomial that represents the revenue for one week, given the price per football.
1. Let's start by defining some variables.
- q: the price in dollars per football.
- R(q): the revenue in dollars for one week.
2. We know that the number of footballs sold per week is given by (3000 - 150q).
3. The revenue can be calculated by multiplying the price per football (q) by the number of footballs sold (3000 - 150q).
R(q) = q * (3000 - 150q)
4. Now we can simplify the expression by distributing q to both terms inside the parentheses.
R(q) = 3000q - 150q^2
5. This is the simplified polynomial that represents the revenue for one week.
To find the weekly revenue if the price is $8 for each football, substitute q = 8 into the polynomial.
R(8) = 3000(8) - 150(8)^2
Compute the expression:
R(8) = 24000 - 150(64)
R(8) = 24000 - 9600
R(8) = 14400
Therefore, the weekly revenue would be $14,400 if the price for each football is $8.