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Math question help!!! ?
A medical equipment industry manufactures X-ray machines. The unit cost (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function C(x) = 0.4x^2 -96x + 24,863. What is the minimum unit cost?
Do not round your answer
3 Answers
- 1 week ago
$19,103
You just take the derivative: dy/dx=0.8x-96
Solve for x in that equation to get 120
That is the number of machines that you need to make.
Plug that number into your first formula to find the cost.
The minimum unit cost is $19103
Alternatively you can just use an online graphing calculator such as desmos and find the minimum y value.
Cheers
Ps I wish that yahoo answers would stay open so that I can find homework answers in the future as well.
- llafferLv 71 week ago
The "x" that gives the minimum unit cost can be found by solving for the zero of the first derivative:
C(x) = 0.4x² - 96x + 24863
C'(x) = 0.8x - 96
0 = 0.8x - 96
-0.8x = -96
x = 120
Now that we know that the 120th unit cost is the cheapest, we can find the cost of this unit by solving for C(120):
C(x) = 0.4x² - 96x + 24863
C(120) = 0.4(120)² - 96(120) + 24863
C(120) = 0.4(14400) - 11520 + 24863
C(120) = 5760 - 11520 + 24863
C(120) = $19,103
