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?
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.
