The marginal cost function of manufacturing x units of a product is 5+16x – 3x2 . The total cost of producing 5 items is GHC500. Find the total cost
Question
The marginal cost function of manufacturing x units of a product is 5+16x – 3x2 . The total cost of producing 5 items is GHC500. Find the total cost
Solution
To find the total cost of manufacturing x units of a product, we need to integrate the marginal cost function. The marginal cost function is the derivative of the total cost function, so to find the total cost function, we integrate the marginal cost function.
The marginal cost function is 5 + 16x - 3x^2.
∫(5 + 16x - 3x^2) dx = 5x + 8x^2 - x^3 + C
We know that the total cost of producing 5 items is GHC500. We can use this information to solve for C.
500 = 5(5) + 8(5)^2 - (5)^3 + C 500 = 25 + 200 - 125 + C 500 = 100 + C C = 500 - 100 C = 400
So, the total cost function is C(x) = 5x + 8x^2 - x^3 + 400.
Now, you can use this function to find the total cost of producing any number of units.
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