21. Maximum revenue and profit. A company manufactures and sells (x) television sets per month. The monthly cost and price-demand equations are (C(x) = 72,000 + 60x) (p = 200 - frac{x}{30}) (0 le x le 6,000) (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 $5 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?
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To maximize revenue, we find the critical point by taking the derivative of the revenue function and setting it equal to zero: \[R'(x) = 200 - \frac{2x}{30} = 0\] Solving for x, we get \(x = 3000\). This is the production level that will maximize revenue. Step 2: Show more…
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21. Maximum revenue and profit. A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72,000 + 60x and P(x) = 4,000 - 6x/30. Find the maximum revenue. Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. If the government decides to tax the company $5 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?
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A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)=72000=70x and p(x)=300-x/20, 0<x<6000 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 $66 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?
Assume that relative maximum and minimum values are absolute maximum and minimum values. A concert promoter produces two kinds of souvenir shirt; one kind sells for $$ 18,$ and the other for $$ 25 . The total revenue from the sale of $x$ thousand shirts at $$ 18$ each and $y$ thousand at $$ 25 each is given by $$R(x, y)=18 x+25 y$$ The company determines that the total cost, in thousands of dollars, of producing $x$ thousand of the $$ 18 shirt and $y$ thousand of the $$ 25 shirt is given by $C(x, y)=4 x^{2}-6 x y+3 y^{2}+20 x+19 y-12$ How many of each type of shirt must be produced and sold in order to maximize profit?
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