(a) Eagle Electronics manufactures four products that it supplies to the aeronautical firms. Each of the products must pass through the following departments before they are shipped: wiring, drilling, assembly, and inspection. The time required at each department (in minutes) for each unit produced, the unit selling price and the average production cost per unit are summarized in the table below: Department Wiring Drilling Assembly AT521 30 30 30 TM203 60 60 90 FX126 90 120 BZ648 60 90 Product 60 120 Minimize, Subject to Inspection 60 60 30 90 Selling price per unit (S) 300 250 180 200 In the next production run, 150 hours of wiring, 180 hours of drilling, 200 hours of assembly and 250 hours of inspection times are available. By contract, Eagle Electronics must produce at least 200 units of product AT521 and 150 units of product TM203. The demands for products FX126 and BZ648 are less than 100 and 150 units each. Formulate a linear programming model for the above problem. C=$30X1 + $40X 8X + 2X2 160 5X: +4X22 100 X + 2X 290 X 30 X 30 (b) The Whole Food Nutrition Centre uses two bulk grains, A and B to blend a natural cereal. Each kilogram of the cereal mix must have the minimum required amounts of protein, riboflavin, and phosphorus. For Xi kilogram of bulk grain A and X kilogram of bulk grain B, the manager has formulated a linear programing model with the objective of minimizing the total cost as below: Average production cost per unit (S) 250 200 50 100 (Protein) (Riboflavin) (Phosphorus) (i) Graphically illustrate the feasible region for the problem. (ii) Is the feasible region bounded or unbounded? (iii) What is the optimal mix of bulk grains A and B? (iv) What is the minimal cost for this problem? (15 marks) (5 marks) (2 marks) (4 marks) (2 marks) (10 marks)