tititacarly2006
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For Incap T-shirts, the cost of producing x T-shirts can be expressed as C=0.6x2+0.52x+3200.

The revenue they gain can be expressed as R=100x.

At what value of x is the profit (R−C) maximised?

In other words, what is the ideal number of T-shirts to make and sell?

Respuesta :

adioabiola

The value of x in which profit can be maximized is -43.67

Given:

C = 0.6x² + 0.52x + 3200

R = 100x

The profit maximizing value of x = R - C

= 100x - (0.6x² + 0.52x + 3200)

= 100x - 0.6x² - 0.52x - 3200

= 0.6x² + 99.48x - 3200

x = -b ± √b² - 4ac / 2a

= 99.48 ± √99.48² - 4×0.6×-3200

= -99.48 ± √9,896.2704 - 7680 / 1.2

= -99.48 ± √2,216.2704 / 1.2

= -99.48 ± 47.08 / 1.2

x = -99.48 + 47.08 / 1.2

or = -99.48 - 47.08 / 1.2

x = -52.4/1.2 or -146.56 / 1.2

x = -43.67 or -122.13

Therefore, the value of x is -43.67

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