Highland Co. is a manufacturing firm. The company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A

and B. However, the company cannot sell more than 100 units of A per day. Both products use one raw material, of which the maximum daily availability is 240 lb. The usage rates of the raw material are 2 Ib per unit of A, and 4 lb per unit of B. The profit units for A and B are £20 and £50 respectively. a) Formulate a linear programming model for this problem. b) Use the graphical method to find the optimal solution to the following Linear Program. Explain the effect(s) of changing constraint x_1+x_2<30 to x_1+x_2<31 in the above linear program (i.e., part b).[ The manager of the Highland Co. (the above company) wishes to forecast the sales volume of product A in the next period. The company has accumulated the following sales data for the past 10 periods. e) Compute the last value forecast, a four period moving average and an exponential smoothing forecast (a = 0.3) for the above sales data. In each case, estimate the sales volume of product A in period 11. f)Compute the Mean Absolute Errors (MAE) for the results in part (e), and comment on the accuracy of the sales forecast pertaining to each of the three techniques. Explain if selecting a larger value of a would have any effect on the performance of the exponential smoothing method in this case and why.[10% of marks] g) Discuss how the Business Analytics methods could be useful to decision makers inAmazon.