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  • 5 years ago

A liquid form of penicillin manufactured by a pharmaceutical firm is sold in bulk at a price of $200 per unit. If the total production cost (in dollars) for x units is C(x) = 500,000 + 80x + 0.003x^2 and if the production capacity of the firm is at most 30,000 units in a specfied time, how many units of penicillin must be manufactured and sold in that time to maximize the profit?

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  1. anonymous
    • 5 years ago
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    the function fot the profit will be the total selling price minus the total production cost. f(x) = 200x - (500,000 + 80x +0.003x^2) f(x) = -0.003x^2 + 120x -500,000 then to find the value of x which will result in maximum profit, you can use the derivative of f(x) f'(x) = 0 f'(x) = -0.006x + 120 = 0 0.006x = 120 x = 20000 then plug x=20000 into f(x) f(x) = -0.003(20000)^2 +120(20000) -500000 that's the maximum profit

  2. anonymous
    • 5 years ago
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    oh the question is how many penicillin, the answer is 20000 units. i thought you're asked to find the profit , haha. then just forget about plugging x=20000 into the equation

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