PFA

The short-run cost function of a company is given by the equation, TC = 200+55q, where TC is the total cost and q is the total quantity of output, both measured in thousands.
Suppose the company borrows money and expands its factory. Its fixed cost rises by $50,000, but its variable cost falls $45,000 per 1,000 units. The cost of interest (i) also enters into the equation. Each 1-point increase in the interest rate raises costs by $3,000. Write the new cost equation.

For the original cost equation, TC = 200 + 55Q
FC1 = 200
VC1 = 55
If the fixed cost increases by $50,000, then the new fixed cost becomes:
FC2 = 200 + 50,000 = $50,200
VC2 = $45,000/1,000 = $45
Also, Interest Cost IC2 = $3000i
The new cost equation becomes:
TC = 50,200 + 45Q + 3000i