The marginal cost of producing the xth box of canning jars is 7 + x 2 1000 dollars per box. Determine how much is added to the total cost by a change in production from x = 25 to x = 75 boxes.

$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

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