Find the maximum profit and number of units that must be produced and sold in order to yield max profit. Assume revenue, R(x) and cost C(x) are in dollars:
R(x) = 50x-.1x^2 and C(x) = 6x+30

One needs to sell 220 units of the product to earn a maximum profit of $4,870.

Step-by-step explanation:

The revenue is .

The cost is

The profit is given by,

Profit = Revenue - Cost

 ....(1)

To maximize the above profit function in (1) we find its critical points.

To verify this critical point is a point of maximum, we calculate the second derivative of P(x) to get  

Hence from the second derivative test, x = 220 is a point of maximum for P(x).

Substitute x in profit,

One needs to sell 220 units of the product to earn a maximum profit of $4,870.

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step-by-step explanation:

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