Question

1:How much does it cost to produce 900 printed shirts?

2:Determine the profit you will make if you sell 900 printed shirts.

3:Find an expression for P(x).

show solution:​

Answer 1

P(x) = (-0.2x² + 480x - 24480)

Explanation:

1). Expression representing the "Cost" to produce the shirts is,

C(x) = 160x + 24480

Where 'x' represents the number of shirts.

Cost to produce 900 printed shirts will be,

C(900) = 160×900 + 24480

= 144000 + 24480

= Php 168480

2). Revenue generated by selling 900 shirts is,

R(x) = 640x - 0.2x²

For x = 900,

R(x) = 640(900) - 0.2(900)²

= 576000 - 162000

= Php 414000

3). Expression for profit:

Since, Profit = Revenue generated - Cost for production

P(x) = R(x) - C(x)

= (640x - 0.2x²) - (160x + 24480)

= (640x - 160x) - 0.2x² - 24480

= 480x - 0.2x² - 24480

P(x) = (-0.2x² + 480x - 24480)