Find the equilibrium price and equilibrium quantity for the following functions. Demand: x = 100 – 2p and supply: x = 3p – 50

Find the stationary values and stationary points for the function f(x) = 2x³ + 9x² + 12x + 1

For a particular process, the cost function is given by C = 56 - 8x+x² where C is cost per unit and x, the number of unit’s produced. Find the minimum value of the cost and the corresponding number of units to be produced.

A company has to supply 1000 item per month at a uniform rate and for each time, a production run is started with the cost of Rs. 200. Cost of holding is Rs. 20 per item per month. The number of items to be produced per run has to be ascertained. Determine the total of setup cost and average inventory cost if the run size is 500, 600, 700, 800. Find the optimal production run size using EOQ formula.

If u = x²(y–x) + y² (x–y), then show that  \(\frac { \partial u }{ \partial x } +\frac { \partial u }{ \partial y } =-2\left( x-y \right) ^{ 2 }\)