Q = 300−2P −P^2 .
(i) Find the price elasticity of supply if the current price is P = 10.
(ii) What is the percentage change in supply if the price rises by 5%?
(b) A fitness club has 430 members each paying e35 membership fee per month. The club wants to raise this fee, and a market survey predicts that for every price increase of e5 it will lose 30 members. What should the monthly membership fee be to maximize the revenue
+130511 (b) A fitness club has 430 members each paying e35 membership fee per month. The club wants to raise this fee, and a market survey predicts that for every price increase of e5 it will lose 30 members. What should the monthly membership fee be to maximize the revenue
Let x be the number of e5 increases
Revenue = Number of members * Price
Revenue = (430 - 30x)(35 + 5x)
Look at the graph of this function here : https://www.desmos.com/calculator/wwkvbpsbux
Since x has to be an integer number, when x = 3, the revenue = e17000
When x = 4 , the revenue = e 17050
So......the monthly price should be e[35 + 5(4) ] = e 55 and the membership will be [430 - 30(4)] = 310
