The Whitewave dairy company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are...

1. The Whitewave dairy company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 1.5 pound containers, which are then sold to distributors throughout the Northeast. The Regular blend must at least 15% extra sharp cheddar, and the Zesty blend must contain at least 27% extra sharp cheddar. The company has orders for 3500 containers of Regular and 4500 containers of Zesty.

This year, a local dairy cooperative offered to provide up to 7600 pounds of cheese blend 1 for $1.15 per pound and up to 8900 pounds of cheese blend 2 for $1.55 per pound. Cheese blend 1 consists of 90% mild cheddar and 10% extra sharp while cheese blend 2 consists of 65% mild and 35% extra sharp.

The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.18 per container. If each container of Regular is sold for $1.95 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce? Formulate a Linear Programming model to determine these amounts.

2. Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs.

For a new client, Innis has been authorized to invest up to $2.15 million in three investment funds: stock fund A, stock fund B and a money market fund. Each unit of stock fund A costs $40 and provides an annual rate of return of 10%; Each unit of  stock fund B costs $55 and provides an annual rate of return of 14%; each unit of the money market fund costs $110 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis’s risk measurement system, each unit invested in stock fund A has a risk index of 8, each unit invested in stock fund B has a risk index of 9 and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis’s client also specified that at least $300,000 be invested in the money market fund. The amount invested in stock fund A must be at least 25% of the total investment.

3. Setup and solve using Excel’s solver. (submit the Excel file)

Min:                 5Xa + 4Xb + 6Xc + 7Xd

St:                    3Xa + 5Xb ≤ 500 + 0.4(XA+Xb+Xc+Xd)

                        2.8Xa + 5Xd ≥ 400 – 6Xb

                        Xb ≥ 4XA + 5Xc

                        Xa ≥ 8

                        Xa, Xb, Xc, Xd ≥ 0