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The demand equation for a certain commodity is given by the following equation. 1 p=EX218x+9?2,05x5108 Find x and the corresponding price p that maximize revenue. The maximum value of R00 occurs at x = D. Some years ago it was estimated that the demand for steel approximately satised the equation p =245 20x, and the total cost of producing x units of steel was C(x) = 182 + 45x. (The quantity x was measured in millions of tons and the price and total cost were measured in millions of dollars.) Determine the level of production and the corresponding price that maximize the prots. The maximum profit occurs at x= (million tons). Until recently, hamburgers at the city sports arena cost $3.50 each. The food concessionaire sold an average of 25,000 hamburgers on game night. When the price was raised to $4.00, hamburger sales dropped off to an average of 20,000 per night. (a) Assuming a linear demand curve, nd the price of a hamburger that will maximize the nightly hamburger revenue. (b) If the concessionaire had xed costs of $1 ,000 per night and the variable cost is $0.40 per hamburger, find the price of a hamburger that will maximize the nightly hamburger profit. (a) Assuming a linear demand curve, find the price of a hamburger that will maximize the nightly hamburger revenue. The hamburger price that will maximize the nightly hamburger revenue is 35 (Round to the nearest cent as needed.) The average ticket price for a concert at the opera house was $50. The average attendance was 3000. When the ticket price was raised to $55, attendance declined to an average of 2500 persons per performance. What should the ticket price be to maximize revenue for the opera house? (Assume a linear demand curve.) To maximize revenue, the price should be $ per ticket. (Type an integer or decimal rounded to two decimal places as needed. Simplify your answer.)