Question

A company produces and sells shirts. The fixed costs are $7000 and the variable costs are $2 per shirt.

(a) Shirts are sold for $12 each. Find cost and revenue as functions of the quantity of shirts, q. Cost is C(q)= Revenue is R(q)=
(b) The company is considering changing the selling price of the shirts. Demand is q=2000−40p, where p is price in dollars and q is the number of shirts. What quantity is sold at the current price of $12 ? What profit is realized at this price? At the current price, the company sells shirts. The profit realized at his price is $

Answer 1

The total revenue is calculated by multiplying the quantity of shirts by the selling price and the total cost is calculated by adding the fixed costs to the variable costs. The quantity sold at the current price of $12 is found by substituting the price into the demand equation. The profit is calculated by subtracting the total cost from the total revenue.

Step-by-step explanation:

Total Revenue and Total Cost

To calculate the total revenue, we multiply the quantity of shirts, q, by the selling price, which is $12. So, the total revenue function is R(q) = 12q. To calculate the total cost, we add the fixed costs, $7000, to the variable costs, which are $2 per shirt multiplied by the quantity of shirts, q. So, the total cost function is C(q) = 7000 + 2q.

Quantity Sold and Profit

To find the quantity of shirts sold at the current price of $12, we substitute p=12 into the demand equation: q = 2000 - 40(12). Solving this equation gives q = 1520 shirts. To calculate the profit, we subtract the total cost from the total revenue: Profit = R(q) - C(q). Substituting the values gives Profit = 12(1520) - (7000 + 2(1520)). Solving this equation gives a profit of $4840.