Question

Assume that the demand function for tuna in a small coastal town is given by p= 180/( q⁰.⁵) ​(200≤q≤800) where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one month.

(a) Calculate the price (in \$ per Ib) that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month.

Answer 1

To produce a demand of 400 pounds of tuna per month, the town's fishery should charge $9 per pound.

Step-by-step explanation:

To calculate the price that the town's fishery should charge for 400 pounds of tuna per month, we need to solve the demand function equation for p. Substituting q = 400 into the equation, we have:

p = 180/(400^0.5)

Calculating this expression gives us p ≈ 180/20 = 9 dollars per pound. Therefore, the town's fishery should charge $9 per pound of tuna to produce a demand of 400 pounds per month.