Maxima and Minima

The expenditure E_c of a person with income I is given by E_c = (0.000035) I² + (0.045) I. Find marginal propensity to consume (MPC) and marginal propensity to save (MPS) when I = 5000. Also find A (average) PC and A (average)

PS.

A manufacturer can sell x items at a price of ₹ (280 - x) each .The cost of producing items is ₹ (x² + 40x + 35) Find the number of items to be sold so that the manufacturer can make maximum profit.

The total cost function of a firm is `C = x^2 + 75x + 1600` for output x. Find the output (x) for which average
cost is minimum. Is `C_A = C_M` at this output?

Solve the following assignment problem to minimize the cost: 

Find the value of x for which the function `f(x) = x^3 - 3x^2 - 9x + 25` is increasing.

A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q². Find the output for which profit is maximum and also find the profit amount at this output.

For the cost function C = 2000 + 1800x - 75x² + x³ find when the total cost (C) is increasing and when it is decreasing.

A tour operator charges ₹ 136 per passenger with a discount of 40 paise for each passenger in excess of 100. The operator requires at least 100 passengers to operate the tour. Determine the number of passengers that will maximize the amount of money the tour operator receives.