Reference no: EM132866213

A large bakery chain is planning for its flour supply over the next three months. Its requirements are estimated at 100,000 kg, 150,000 kg, and 120,000 kg for month 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 40,000 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 deliver wheat at a specified time and price), and the wheat can be milled into flour for the company's use.

The company forecasts that the market price of flour per hundred kg will be $8.10 at the beginning of month 1, $9.20 for month 2, and $8.60 for month 3. Any flour carried over in inventory from one period to the next will cost $0.50 per hundred kg for storage and other holding costs.

The present price of "wheat futures" is $1.50 per bushel for delivery in month 2 and $1.40 per bushel for delivery in month 3. Assume wheat weighs 25 kg per bushel and costs $0.10 per bushel for milling. Milling yields 60% flour and 40% other products. The other products can be sold at a price of $2.00 per hundred kg.

Formulate algebraically the linear programming model in order to minimize the total cost and help solve the bakery's flour supply problem. Define the decision variables, objective function, and constraints. DO NOT SOLVE.