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2.Una división de ACME fabrica un radiolocalizador. El costo fijo semanal de la división es de $20,000 y el costo variable de


2.Una división de ACME fabrica un radiolocalizador. El costo fijo semanal de la división es de $20,000 y el costo variable de


A division of ACME manufactures a radio pager. The divisions weekly fixed cost is $ 20,000 and the variable cost of producin
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Answer #1

Let the production level be x

Total cost = 20000 + 0.000001x^3 – 0.01x^2 + 50x

Revenue = -0.02x^2 + 150x

Then the profit is Revenue – Total cost = -0.02x^2 + 150x – 20000 -0.000001x^3 +0.01x^2 – 50x

Or,

P = -0.000001x^3 -0.01x^2 + 100x -20000

In order to maximize this we can use calculus where dP/dx = 0

Or

0 = -0.000003x^2 -0.02x + 100

Solving this we get

x = -10000 or 3333.33

Since the value of x cannot be negative the correct answer is 3333.33 units

Rounding to nearest whole number,

The maximum profit will be generated at x = 3333 units

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