The manager of a restaurant found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12. Assume the cost C(x) is a linear function of x, the number of cups produced. a) Find a formula for C(x).(b) What is the fixed cost?(c) Find the total cost of producing 1000 cups.(d) Find the total cost of producing 1001 cups.(e) Find the marginal cost of the 1001st cup.(f) What is the marginal cost of any cup 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.