John's Lawn Moving Service is a small business that acts as a price taker (i.e., \(M R=P\) ). The prevailing market price of lawn mowing is \(\$ 20\) per acre. John's costs are given by \\[ \text { total cost }=. l q^{2}+l O q+50 \\] where \(q=\) the number of acres John chooses to cut a day. a. How many acres should John choose to cut in order to maximize profit? b. Calculate John's maximum daily profit. c. Graph these results and label John's supply curve.

#Short Answer# To maximize his profit, John should mow the optimal quantity of acres, which can be calculated by setting the marginal cost (MC) equal to the marginal revenue (MR). In this situation, it is given that MR is \$20. First, find the MC by taking the derivative of the total cost (TC) function with respect to the quantity (q). By setting MC equal to MR and solving for q, we can determine the optimal quantity for John to mow. Then, calculate John's total revenue (TR) and the profit at the optimal quantity. Finally, graph the marginal cost, marginal revenue, and supply curve to visualize the results. The supply curve represents the relationship between the price and quantity supplied, and the intersection of MC and MR curves indicates the optimal quantity for John to maximize his profit.