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A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that the daily marginal cost function associated with producing these toaster ovens is given by C'(x) = 0.0006x2 − 0.12x + 22 where C'(x) is measured in dollars per unit and x denotes the number of units produced. Management has also determined that the daily fixed cost incurred in the production is $900. (a) Find the total cost incurred by Ditton in producing the first 300 units of these toaster ovens per day.

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Answer:

$7,500

Step-by-step explanation:

Integrating the daily marginal cost per unit function (C'(x)) at the interval from 0 to 300 units gives us the total variable cost incurred by Ditton in producing he first 300 units.

[tex]C'(x) = 0.0006x^2 -0.12x+ 22\\\int\limits^{300}_0 {C'(x)} \, dx = C(x)|_0^{300}  = (0.0002x^3 -0.06x^2 +22x)|_0^{300} \\C(300) - C(0) = (0.0002(300)^3 -0.06(300)^2 +22(300)) -  (0.0002(0)^3 -0.06(0)^2 +22(0)) \\C(300) - C(0) =6,600[/tex]

The variable cost incurred is  $6,600

The total cost is given by sum of the variable cost and the fixed cost:

[tex]C= 6,600+900\\C=\$7,500[/tex]

The total cost incurred by Ditton in producing the first 300 units of these toaster ovens per day is $7,500.

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