Calculate the elasticity of demand for the demand schedule by using differential calculus method P = 60 - 0.2Q where price is (i) zero, (ii) Rs.20, (iii) Rs.40

Find the solution of the equation system.
7x₁ - x₂ - x₃ = 0
10x₁ - 2x₂ + x₃ = 8
6x₁ + 3x₂ - 2x₃ = 7

Mr.Anbu purchased 2 pens, 3 pencils and 1 note book. Mr.Barakath purchased 4 pens, 3 pencils and 2 notebooks. Mr.Charles purchased 2 pens, 5 pencils and 3 notebooks. They spent Rs.32, Rs.52 and Rs.60 respectively. Find the price of a pen, a pencil and a notebook.

A manufacturer estimates that, when units of a commodity are produced each month the total costs will be TC(Q) = 128 + 60Q + 8Q². Find the marginal cost, average cost, fixed cost, variable cost, average fixed cost and average variable cost.

Given the demand function P_d = 2S - Q² and the supply function p_s = 2Q + 1. Assuming pure competition, find (a) consumers surplus and (b) producers surplus. (P_d = Demand price; P_s = Supply price)