Assume that the demand function for tuna in a small coastal town is given by
p = 180/ q^0.5
(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 that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month.

Question

Assume that the demand function for tuna in a small coastal town is given by
p = 180/ q^0.5
    (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 that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month.

anonymous · Answer

Someone please help me with this problem

valpey · Answer

You will need to plug the quantity "400 pounds" into the equation:
$$price=\frac{180}{\sqrt{quantity}}$$

valpey · Answer

q^0.5 is the same as the square root of q.

valpey · Answer

You may see that if q is larger p must be smaller (which makes sense because if the price is lower, it is easy to sell more tuna) If the price is higher, it will be harder to sell and the quantity sold will be lower. Eventually you will probably be asked, "what is the optimal price to maximize revenue" or something. Revenue will be equal to price*quantity.