The Pentium Company makes three types of pens: ballpoints, mechanical pencils and fountain pens. These are made from plastic, chrome and steel and the table gives the ounces of each of these ingredients that are used to make one pen. The company also uses labour, packaging and quality control techniques in the production process and the profitability of these pens, shown in the table are derived from the accounting process after all inputs are taken into account. For example, plastic cost $5.00 per ounce and this is taken into account to get the profit. Profit per unit Plastic Chrome Stainless Steel Ballpoints Mechanical Fountain Pencils $3 1.2 0.8 2 $3 1.7 0 3 Pens $5 1.2 2.3 4.5 Available (ozs) 1,000 1,200 2,000 i. Write the decision variables that will be used in the model and state the decision that the manager must make. ii. Write the objective function and state clearly what Pentium's objective is. iii. Write down all the constraints that should be used to solve the problem presented. iv. Explain what the solution would mean in terms of the decision variables and the objective function.