Question

Assume that the demand for tuna in a small coastal town is given by p = 550,000 q1.5 where q is the number of pounds of tuna that can be sold in a month at p dollars per pound. (a) What is the monthly revenue as a function of the demand for tuna? R(q)= Incorrect: Your answer is incorrect. (b) Assume that the town's fishery wishes to sell at least 5,000 pounds of tuna per month. This means you are studying the revenue function on the domain [5000,∞). Does the monthly revenue function have any stationary points? Correct: Your answer is correct. Does the monthly revenue function have any singular points? Correct: Your answer is correct. Use the First Derivative Test to determine if the monthly revenue is increasing or decreasing on the domain [5000,∞). The monthly revenue is Incorrect: Your answer is incorrect. on the domain [5000,∞). (c) From your analysis above, how much tuna should the fishery sell per month in order to maximize monthly revenue? q = Incorrect: Your answer is incorrect. lb How much should they charge for tuna in order to sell that much fish? (Round your answer to the nearest cent.) p = Incorrect: Your answer is incorrect. dollars per lb What will be its resulting maximum monthly revenue? (Round your answer to the nearest dollar.) $ Incorrect: Your answer is incorrect. per month

Answer 1

Answer: he town wants to sell at least 5000 lbs per month, so (a) should be 550000/5000^1.5=$1.55 per pound (b) comes straight from answer (a) For (c), multiply 1.55 dollars/lb * 5000 lbs of tuna= $7750.