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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
Answer:
The total cost is $[tex]1716[/tex]
Explanation:
[tex]$C^{\prime}(x)=-4 / 25 x+59$[/tex]
Taking integral on both sides
[tex]integral $\left(C^{\prime}(x)\right)=$ Integral $(-4 / 25 x+59)$[/tex]
[tex]$C(x)=-4 /\left(25\times2\right) x^ 2+59 x+c$[/tex]
The cost of producing units is:
[tex]$C(160)=-4 / 50(160)^ 2+59(160)+c$[/tex]
[tex]$C(160)=-4 / 50(160)^2+59(160)+c$[/tex]
Since we know that cost of producing dresses is hence,
[tex]$7392=-2048+9440+c$[/tex]
[tex]$c=0$[/tex]
Hence the above function can be written as:
[tex]$C(x)=-4 / 50 x^ 2+59 x$[/tex]
Now we will calculate the cost of producing, units:
[tex]$C(220)=-4 / 50\left(220^ 2\right)+59(220)$[/tex]
[tex]$=\$ 9108$[/tex]
We already know that the cost of producing units in hence,
The cost of producing st to th units will be,
[tex]$\mathrm{C}(220)-\mathrm{C}(160)=9180-7392$[/tex]
[tex]$=\$ 1716$[/tex]
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