Please show work A store can sell 16 bicycles per week at a

Please show work.

A store can sell 16 bicycles per week at a price of $400 each. You have estimated that for each $10 price reduction you can sell two more bicycles per week. The bicycles cost your store $200 each. Questions:Find a function for each of these: (let x be the number of deductions)

a. price b. quantity c. revenue d. cost e. profit

2. Find the number of deductions that will maximize your profit.

3. What price are you going to set your bicycles at? What quantity will you sell, what is your cost, your revenue, and profit at this price?

4. You have done some shopping around and found that you can buy the bicycles from another wholesaler for $150 each. Now what price are you going to sell them at?

5. Cycling has all of a sudden become very popular. Demand is up and you can now sell 25 bicycles at the original $400. How does this change your price to maximize profit?

Solution

let x be no. of deuctions

a) Selling Price = 400 -10x

b) Quanttity = 16+2x

c) Revenue = seelig price x quatity = (400-10x)(16 +2x)

d) Cost = 200(16+2x)

e) Profit = Revenue -Cost = (400-10x)(16 +2x) -   200(16+2x)

= (16 +2x)( 400 -10x -200) = (16 +2x)( 200-10x) = -20x^2+400x +3200 -160x

= -20x^2+ 240x +3200

f) maximumu profit occurs at x= -b/2a = -240/(-2*20) = 240/40 = 6

So, at x=6

a) Selling Price = 400 -10*6 = $ 340

b) Quanttity = 16+2x = 16+2*6 = 28

c) Revenue = seelig price x quatity = (400-10x)(16 +2x) = $9520

d) Cost = 200(16+2x) = $ 5600

e) Profit = Revenue -Cost = (400-10x)(16 +2x) -   200(16+2x) = $9520- $ 5600 = $ 3920