Question

A company produces and sells shirts. The fixed costs are $$\$ 7000$$ and the variable costs are $$\$ 5$$ per shirt. (a) Shirts are sold for $$\$ 12$$ each. Find cost and revenue as functions of the quantity of shirts, $q$. (b) The company is considering changing the selling price of the shirts. Demand is $q=2000-40 p$, 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? (c) Use the demand equation to write cost and revenue as functions of the price, $p$. Then write profit as a function of price. (d) Graph profit against price. Find the price that maximizes profits. What is this profit?

          A company produces and sells shirts. The fixed costs are $$\$ 7000$$ and the variable costs are $$\$ 5$$ per shirt.
(a) Shirts are sold for $$\$ 12$$ each. Find cost and revenue as functions of the quantity of shirts, $q$.
(b) The company is considering changing the selling price of the shirts. Demand is $q=2000-40 p$, 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?
(c) Use the demand equation to write cost and revenue as functions of the price, $p$. Then write profit as a function of price.
(d) Graph profit against price. Find the price that maximizes profits. What is this profit?

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