Question

Hey! A step by step explanation on this would be great! Thanks! (25 Points)

Answer 1

Step-by-step explanation:

We find the stationary point of (20 + 2x)(1200 - 60x),

where x is the unit rate of increase/decrease.

d/dx [(20 + 2x)(1200 - 60x)]

= d/dx (-120x² + 1200x + 24000)

= -240x + 1200.

When d/dx [(20 + 2x)(1200 - 60x)] = 0,

We have -240x + 1200 = 0. => x = 5.

Price per shirt that maximise revenue

= $20 + $2x = $20 + $2(5) = $30.

Maximum revenue

= (20 + 2(5))(1200 - 60(5))

= $30 * 900 = $27,000.