3. Problem 3 45. The demand for a perishable item over the next four months is 400,300,420, and 380 tons, respectively. The supply capacities for the same months are 500,600,200, and 300 tons The purchase price per ton varies from month to mininth and is estimated at $100,$140,5120. and $150, respectively. Because the item is perishable, a current month's supply must be consumed within 3 months (starting with current month). The storage cost per ton per month is $3. The nature of the item does not allow back-ordering Solve the problem as a transportation model, and determine the optimum delivery schedule for the item over the next 4 months a) Formulate the problem as a transportation problem b) Use northwest method to find an initial solution c) Use least cost method to find an initial solution d) Use Vogel Algorithm to find initial solution e) Using the initial solution with the lowest cost use the method of multiplier to fond the optimal solution