Problem 4 (24 points) A large bakery chain is planning for its flour supply over the next three months. Its requirements are estimated at 130,000 kg, 170,000 kg, and 110,000 kg for months 1, 2 and 3, respectively. It expects to have carryover stock (i.e. beginning inventory) of 20,000 kg going into month 1, and wants an inventory of at least 60,000 kg at the end of the third month. It can meet its requirements by purchasing flour on the market (for immediate use or for inventory for future use) or it can buy "wheat futures" (a promise by a supplier to provide wheat at a specified time and price) which it can have milled into flour for its use. The company forecasts that the price of flour per hundred kg will be $9.10 for delivery at the beginning of month 1, $10.20 for month 2 delivery, and $9.60 for month 3 delivery. Any flour carried over in inventory from one period to the next will cost $0.75 per hundred kg for storage and other holding costs. The present price of wheat for future delivery is $2.50 per bushel for delivery in time to meet only the month 2 requirements and $2.40 per bushel for delivery in time to meet only the month 3 requirements. Assume wheat weighs 25 kg per bushel and costs $0.50 per bushel for milling. Milling yields 60% flour and 40% other products. The other products can be sold at a price of $3.00 per hundred kg. Formulate algebraically the linear programming model in order to minimize the total cost and help to solve the bakery's flour supply problem. Define the decision variables, objective function, and constraints. DO NOT SOLVE