A manufacturer sells lamps at six dollars each and sells 3000 each month. For each one dollar that the price is increased, 1000 fewer lamps are sold each month. It costs 4 dollars to make one lamp. What price should lamps be sold at to maximize profit

Price it will be sold to make maximum profit = $6.5 each

Explanation:

The challenge is to maximize profit.

We can assign to be the number of dollars obtained per unit price per flashlight.

Recall:

Profit = Revenue - Cost

Revenue = price charged x number sold =

Cost = cost to produce a unit x number of units produced

Profit =

At the point of maximum profit, the change in profit with respect to price will be = 0. In mathematical terms, the derivative of the profit will be = zero

∴

from this, we can see that at maximum profit, x = 0.5

∴ Price it will be sold to make maximum profit = $6.00 + 0.5 = $6.5 each