e) A manufacturer produces three products: Product A, Product B and Product C. To be able to produce each product he uses a combination of three distinct inputs namely Input I, Input II and Input III the supply of which is currently at 730, 350 and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3 units of Input II and 4 units of Input III to be produced. Similarly, each unit of Product B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5 units of Input I, 1 unit of Input II and 3 units of Input III. (i) Let a, b and c represent the number of units produced of Products A, B and C respectively. The manufacturer must decide what quantity of each product to produce so that his entire supply of inputs is utilized. Formulate his/her decision in the form of a system of three linear equations in the variables a, b and c. [3 marks] (ii) Rewrite the above system of linear equations in the matrix form Ax = b. [2 marks] (iii) Hence or otherwise, determine how many units of product B that can be manufactured. [5 marks]