Find the price that will maximize profit for the demand and cost functions, where p is the price, x is the number of units, and C is the cost. Demand Function Cost Function p = 46 − 0.1 x C = 31x + 500

The correct answer is 38.5

Step-by-step explanation:

Cost function is given by C = 31x + 500

Demand function is given by p = 46 − 0.1 x ,

where p is the price, x is the number of units, and C is the cost.

Revenue function (R) is given by p × x = 46x - 0.1

Profit π = R - C

⇒ π = 46x - 0.1 - 31x + 500.

To maximize profit we find π and equate it to zero.

⇒ 46 - 0.2x -31 = 0

⇒ 15 = 0.2x

⇒ x = 75.

Price at quantity x is equal to 75 = 46 - 7.5 = 38.5

Thus the price at which the profit maximizes for the given demand and price functions is 38.5.

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step-by-step explanation: