Problem #1 - Maximizing Profit A small company makes custom surfboards. They have found that if they sell the surfboards for $100 the demand is 100 boards. If they sell the surfboards for $80, the demand is 140 surfboards. a. Find a linear demand equation showing the number of surfboards, q, demanded as a function of the selling price p and then use the demand function to build the revenue function. b. If the marginal cost to produce each surfboard is $40 and there are fixed costs of $1000, report the cost and profit functions as a function of the price p. c. Determine what value of p will maximize profit? What is the maximum profit? How many surfboards are sold at that price?