Question

The cost of producing a plastic toy is given by the function C(x) = 8x + 25, where x is the number of hundreds of toys. The revenue from toy sales is given by R(x) = −x2 + 120x − 360. Since profit = revenue − cost, the profit function must be P(x) = −x2 + 112x − 385 (verify). How many toys sold will produce the maximum profit? What is the maximum profit?

Answer 1

for maximum profit derivative of profit function is zero

hence take derivative

sell to get maximum profit

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maximum profit is

.......maximum profit

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NOTE: you can also find it through vertex of parabola , that give you maximum point