Question

A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72,000 + 40x and p(x)= 300 - 500SX S 9000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company 54 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set? (A) The maximum revenue is S 675000 (Type an integer or a decimal.) (B) The maximum profit is when sets are manufactured and sold for each (Type integers or decimals.) (C) When each set is taxed at $4, the maximum profit is $ when sets are manufactured and sold for (Type Integers or decimals.) each

Answer 1

Drop a comment if you have any further doubts regarding the solution

UPVOTE PLEASSEEE :D

Also I assume you've solved the first part so I didn't attempt it

CCX) = 72,000 + 40x 300 - X 0 < x < gooo 30 Revenue = (x).(p(x)] 300x - x2 30 Profit = = revenue - 300 x-x2 30. cost - ( 72,000+ 40x) PIX) = 260X - x2 - 72,000 30 260x - x - 72,000 p'(x) = 0 For maximum profit, p'(x) = 260 - 34 x) = 260a 2x to 30 O = 260 - X 15 260 (15) [x = 3,900 profit (x = 3, 900) = 26013900) – (3,90072 - 72,000 = 942,000 - 509,000 = 435,000 300 - = 1 ayo 3,900 30

182 maximum profit when mice = 435,000 € = 3900 units = 170 $ 1c) for profit - 260x – X2 - 72,000 - 4x 30 Tax Deduction PLX) = 256x - x2 - 72,000 30 For maxm Prix) = 256 - 2x 30 256 X 15 x = = 3,840 Pelit x= 3,840 ) = 256( 3840) - (3840) 72000 3 911,040 - 431, 520 = 419, 520 (x) = 300 - 3840 s 172 maximum profit = 419, szo & when = 3,840 unia price = 172 $