A manufacturer can produce a color pen at a cost of $3. the color pens have been selling for $5 per pen and at this price, consumers have been buying 4000 pens per month. the manufacturer is planning to raise the price of the pens and estimates that for each $1 increase in price, 400 fewer pens will be sold each month. at what price should the manufacturer sell the pen to maximize profit? what is the maximum profit?

Question

Mathematics

Ebony

15 December, 04:06

A manufacturer can produce a color pen at a cost of $3. the color pens have been selling for $5 per pen and at this price, consumers have been buying 4000 pens per month. the manufacturer is planning to raise the price of the pens and estimates that for each $1 increase in price, 400 fewer pens will be sold each month. at what price should the manufacturer sell the pen to maximize profit? what is the maximum profit?

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Answers (1)

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Quintin · Answer 1

Let x be the number of increases of $1 a month.

Let y be the maximum profit.

The profit before the price increases:

$5-$3=$2

The profit when increasing the price:

y = (2+x x 1) (4000-400x)

y = 8000-800x + 4000x - 400x2 (x2: x square)

The vertex:

x = - 3200 / (-400 x 2) = 4

=> y = 14400

The price can maximize the profit is:

p = 3 + 2 + 4x1 = 9

The price can maximize the profit is $9

The maximum profit is $14400.