Question

A clothing company determines that its marginal cost, in dollars per dress, is given by the function below. The total cost of producing the first 160 dresses is $7072
Find the cost of producing the 161st through the 200th dress

C'(X)= - 3*+ 57, for x 5 350

The total cost is

Answer 1

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Q) A clothing company determines that its marginal? cost, in dollars, per? the dress is given by the function below. The total cost of producing the first 160 dresses is ?$7392. Find the cost of producing the 161st through the 220th dress. C'(x)= -4/25 x +59, for x<= 360 the total cost is? round to the nearest cent.

Answer:

$1716

Step-by-step explanation:

C'(x) = -4/25 x +59

Taking integral on both sides

integral(C'(x)) = Integral (-4/25 x + 59)

C(x) = -4/(25*2) x^2 +59x +c

The cost of producing 60 units is:

C(160) = -4/50 (160)^2 + 59(160) + c

Since we know that cost of producing 160 dresses is $7392 hence,

7392 = -2048 + 9440 + c

c = 0

Hence the above function can be written as:

C(x) = -4/50 x^2 + 59x

Now we will calculate the cost of producing, 220 units:

C(220) = -4/50 (220^2) + 59(220)

= $9108

We already know that the cost of producing 160 units in $7392 hence,

The cost of producing 161st to 220th units will be,

C(220) -C(160) = 9180 - 7392

= $1716