Questions Q1 product mix

The Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of labour hours in the carpentry department, and a certain number of labour hours in the painting department. Each table takes 4 hours of carpentry work and 2 hours of painting work. Each chair requires 3 hours in carpentry time and 1 hour in painting. During the current production period, 240 hours of carpentry time and 100 hours of painting time are available. The marketing personnel are confident that they can sell all the tables that are made. However, due to an existing inventory of chairs, they want Flair to make no more than 60 new chairs. Each table sold results in a profit contribution of $7, and each chair sold yields a profit contribution of $5. Flair Furniture is to determine the best possible combination of tables and chairs to manufacture in order to attain the maximum profit. The firm would like this product mix situation formulated as an LP problem.

a)Formulate using LP

b) Solve graphically

c) Solve in Excel Investment selection

Q 2 (a) The CWD Brokerage firm has just been instructed that by one of its clients to invest $500,000 for her – money recently obtained through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines:

1. Municipal bonds should comprise at least 25% of the investment.

2. At least 30% of the funds should be placed in a combination of electronic firms, aerospace firms and drugs manufacturers.

3. No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high –yielding nursing home stock.

Subject to these restraints, the client’s goal is to maximise projected return on investments. The analysts at CWD, aware of these guidelines, prepared a list of quality stocks and bonds and their corresponding rates of return.

Investment Projected Rate of Return (%)

Los Angeles Municipal Bonds 5.3

Thompson Electronics, Inc. 6.8

United Aerospace Corp. 4.9

Palmer Drugs 8.4

Happy Days Nursing Home 11.8

Formulate this portfolio selection problem using linear programming

Q3 –product mix blending CWD agro. produces two pepper sauces, Hot Scorpion and Mad Devil . These sauces are both mace by blending two ingredients, A and B. A certain level of flexibility is permitted in the formulae for these products. The allowable percentages, along with revenue and cost data, are given in the following table. Up to 80 quarts of A and 60 quarts of B could be purchased. Saddam can sell as much of these sauces as it produces. Formulate an LP whose objective is to maximise the net profit from the sale of the sauces.

Sauce Ingredient A Ingredient B Sales Price per quart (s)

Hot Scorpion At least 35% At least 50% 7.00

Mad Devil At most 70% At least 40% 5.70

Cost per Quart $3.20 $5.00