You just opened your new bagel shop. Your financial advisors studied the market and gave you the following equation for supply as a function of price:
S(p) = 60p
and the following equation for the demand as a function of price:
D(p) = 120 - 3p.
You wish to determine your revenue as a function of price. To get the revenue, you multiply the price per unit by the quantity of bagels sold. You use the demand function to estimate how many bagels you can sell.
a. What is the formula for the revenue function? Remember: You do not have to have something in front of all these equal signs, you can add more if you need to.
b. What price should you set to maximize revenue?
c. Consider the following profit function: Π(q) = -q2 + 6q + 100
For what values of q will you breakeven?