QUESTION TWO Explain the limitations of linear programming and give alternative approaches to address them (10 marks) (b) The planning committee of a bank makes monthly decisions on the amount of funds to allocate to loans and to government securities. Some of the loans are secured (backed by collateral such as a home or automobile), and some are unsecured. A list of the various types of loans and their annual rates of return as shown below: Annual Rate of Return Type of Investment Secured loans: Residential morgage (x1) Commercial morgage (x2) Automoble (x3) Home improvement (x) Unsecured loans: Vacation (xs) Student (X) Government securities (x2) 11 12 15 13 17 10 9 b) Maximize utility U=2xy subject to a budget constraint equal to 3x +4y = 90 by: i) Finding the critical values x, y anda and ii) Using the bordered Hessian H to test the second order condition. Find the price-demand equation for a particular brand of toothpaste at a supermarket chain when the Demand is 5 tubes per week at $2.35 per tube, given that the marginal price-demand function P'(x), for x number of tubes per week is given as: c) -0.01% P'(x)=-0.015e If the supermarket chain sells 100 tubes per week, what price should it set? b) Maximize utility U =2xy subject to a budget constraint equal to 3x +4y= 90 by: i) Finding the critical values x,y and 2 and Using the bordered Hessian to test the second order condition. Find the price-demand equation for a particular brand of toothpaste at a supermarket chain when the Demand is 5 tubes per week at $2.35 per tube, given that the marginal price-demand function P(x), for x number of tubes per week is given as: c) -0.01 P'(x)=-0.015e If the supermarket chain sells 100 tubes per week, what price should it set? QUESTION FOUR: a) In a monopolistic competition, producers must determine the price that will maximize their profit. Assume that a producer offer two different brands of a product, for which the demand functions are: Q. = 14 -0.25P, Q, = 24 -0.5P And the joint cost of function is: TC = Q} +5Q, Q, +Q Find the Profit Maximizing level of output, the price that should be charged for each brand and the profits. 3