SOLUTION: The cost of production of an item is represented with the following equation: C(x) = 7x + 10. The revenue function for this item was determined to be R(x) =

SOLUTION: The cost of production of an item is represented with the following equation: C(x) = 7x + 10. The revenue function for this item was determined to be R(x) = - 2x2 + 59x. What is

Question 1197165: The cost of production of an item is represented with the following equation: C(x) = 7x + 10. The revenue function for this item was determined to be R(x) = - 2x2 + 59x. What is the maximum amount of profit that can be made at the point where the number of items is the greatest to maximize profit?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The cost of production of an item is represented with the following equation:

The revenue function for this item was determined to be:

What is the maximum amount of profit that can be made at the point where the number of items is the greatest to maximize profit?

Profit is revenue minus cost. This means there is a function, , that is profit.

the maximum amount of profit that can be made at the vertex (parabola is opening down)
..........write in vertex form
......complete square
............ coefficient of is , so

=> vertex is at (,)
the maximum amount of profit is at

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