Problem 3 (30 points) Sound Electronics, Inc. produces a battery-operated tape recorder at plants located in Martinsville, North Carolina; Plymouth, New York; and Franklin, Missouri. The unit transportation cost for shipments from the three plants to distribution centers in Chicago, Dallas, and New York are as follows: FROM Martinsville Plymouth Franklin CHICAGO 1.45 1.10 1.20 DALLAS NEW YORK 1.60 1.40 2.25 0.60 1.20 1.80 After considering transportation costs, management has decided that under no circumstances will it use the Plymouth-Dallas route. The plan capacities and distributor orders for the next month are as follows PLANT CAPACITY (units) Martinsville 400 Plymouth 600 Franklin 300 DISTRIBUTOR ORDERS (units) Chicago 400 Dallas New York 400 400 Because of different wage scales at the three plants, the unit production cost varies from plant to plant. Assuming the costs are $29.50 per unit at Martinsville, $31.20 per unit at Plymouth, and $30.35 per unit at Franklin, find the production and distribution plan that minimizes production and transportation costs. a) (5 points) Write a linear programming formulation of this problem. b) (10 points) Find the optimal solution by using Excel. Include the computer output. c) (15 points) Prepare a report using PowerPoint. The report should include: (2 points) -Introduction to the problem (2 points) -Decisions to be made (5 points) -Formulation (1 point) -Solution Method (Linear programming using SOLVER) (5 points) -Solution: overall cost, how many units should be produced at each plant and how many units should be shipped from each plant to each distributor.