EXAMPLE 2.6-27 (Product Mix Problem) Consider a company that must produce two products over a production period of three months of duration. The company can pay for materials and labour from two sources: company funds and borrowed funds. The firm faces three decisions: 1. How many units should it produce of product I? 2. How many units should it produce of product 2 ? 3. How much money should it borrow to support the production of the two products ? In making these decisions the firm wishes to maximize the profit contribution subject to the conditions stated below: f19 (1) Since the company's products are enjoying a seller's market, it can sell as many units as it can produce. The company would, therefore, like to produce as many units as possible subject to production capacity and financial constraints. The capacity constraints, together with cost and price data, are given in the table below: Product Selling price Cost of Required hours per unit in deptt. Runit) production A B 1 14 10 0.5 0.3 0.2 2 17 8 0.3 0.4 0.1 Available hours per production 500 400 200 period of three months (11) The available company funds during the production period will be 3 lakhs. (1) A bank will give loans upto 2 lakhs per production period at an interest rate of 20 per cent per annum provided the company's acid (quick) test ratio is at least I to I while the loan is outstanding Take a simplified acid test ratio given by Surplus cash on hand after production + Accounts receivable Bank borrowings + Interest accrued thereon (iv) Also make sure that the needed funds are made available for meeting the production costs. Formulate the above as linear programming problem. [C.A. Nov., 1992)