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 5000 items as $400,000 and the cost to produce 12,000 items as $750,000. (a) Find a formula for C(x).(b) Find the fixed cost.(c) Find the total cost to produce 30,000 items.(d) What is the marginal cost of the items to be produced in this plant and what does this mean to the manager?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.