Question

A company Inc. finds that it costs $200 to produce each motorized scooter and that the forced costs are $1,000 per day yielding the cost function C(x) = 200x + 1,000 The price is given by p=600 - 5x, where p is the price in dollars at which exactly x scooters will be sold. Find the quantity of scooters that the company Inc. should produce and the price it should charge to maximize profit. Find the maximum profit How many scooters should the company produce to maximize profit? scooters What price should the company charge to maximize profit? What is the maximum profit?

Answer 1

cost of x scooters = 200x+100v = C(X) Selling Adice of scooter = p = 600-sx Selling Price of a scooters = x (600-5x) 5(x) = 600x-532 (say) Total Profit as a function of a (no. of scooters) can be taken as = S(x) - CEx) say f(x) = S(x) - C(x) fox) (600x-502)-(2008 +1000) -5x² +4oox - 1000 fixes Now we have to maximize this function feas. f'(x) = -5(2x) + 400(1)-0 (by using & an = n-x3-1) dre f'(x) = -10 ~ +400 → Now Put f'(x)= 0 - 10x+400 = 0 x = 40o = 40 3=40 10 f”(x) = -10(1) +0 = -10 <0 (at 2=40) "f" (2) To Hence f(x) has local maxima at x=40. at x=40 flag will be maximum- - f(x)/max f (x) -5(403 +400(40)-1000 lata=40 = 600 f(x) max = -5*1600 + 16000 - 1000 -8000 +16000 - 1000 = 7000 $ Price Pat (x=40) = 600-5(40). 200 = 400 $ Answerto 40 scooters should be col company Produce to maximize profit. Price 1400 $ should the company charge to Maximise profit. Maximum Profit 7000 $