You didn't write the equation properly so it is hard for me to understand the equation, however, I am sharing a similar question with you with the help of which you will be able to tackle these types of questions
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
