In deciding whether to set up a new manufacturing plant, company analysts have decided that a linear function is a reasonable estimation for the total cost C(x) in dollars to produce x items. They estimate the cost to produce 10,000 items as $547,500, and the cost to produce 50,000 items as $737,500.

(a) Find a formula for C(x).

(b) Find the fixed cost.

(c) Find the total cost to produce 100,000 items.

(d) Find the marginal cost of the items to be produced in this plant and what does this mean to the manager?