Answer: $485.417
Explanation:
Given the function ;
Marginal cost of (x) = (7 + (x^2/1000))
To determine change in total cost, we have to calculate the total cost at x=25 and x=75.
Note Marginal cost function is the first derivative of the total cost function. Therefore to revert the marginal cost function back to the total cost function, we integrate the marginal cost function.
Now integrate the function f(x) = (7 + (x^2/1000))
Mathematically,
∫f(x)dx = ∫(7+x^2/1000)dx
∫(7+x^2/1000)dx=∫7dx + ∫x^2/1000dx
= 7x + x^3/3000
Therefore, the total cost function is
Total cost(x) = 7x + x^3/3000
Therefore, at x = 25
Total cost =(7×25)+((25^3)/3000)
Total cost =175 + 5.208 = $180.208
At x=75
Total cost =(7×75)+((75^3)/3000)
Total cost = 525+140.625=$665.625
Change in cost = $665.625 - $180.208 = $485.417
