Mathematics economics

University of Venda SUBJECT: MAT 1645 ASSIGNMENT 01 MARKS. 45 DUE DATE: 21 NOVEMBER 2020 1. The demand function of a good is given by Q = 1000e.0.28. Fixed costs are 100 and the variable costs are 2 per unit. (a) Show that the profit function is given by IT = 1000Pe 0.25 - 2000e-0:28 - 100. (5) (b) Find the price needed to maximize profit. (10) 2. A firm's production function is given by Q = L 2e-DOTL Find the value of L that maximizes the average product of labour. (13) 3. Find the output needed to maximize profit given that the total cost function and total revenue functions are TR = 100 (Q + 10) and TC = 2Q respectively. (13) 4. A firm estimate that the total revenue received from the sales of Q goods is given by TR = In (1 + 1000Q2). Calculate the marginal revenue when Q = 10. (4)