Assignment 1
1. When Molly Lai purchased the Clean Clothes Corner Laundry, she thought that because it was in a good location near several high-income neighborhoods, she would automatically generate good business if she improved the laundry's physical appearance. Thus, she initially invested a lot of her cash reserves in remodeling the exterior and interior of the laundry. However, she just about broke even in the year following her acquisition of the laundry, which she didn't feel was a sufficient return, given how hard she had worked. Molly didn't realize that the dry-cleaning business is very competitive and that success is based more on price and quality service, including quickness of service, than on the laundry's appearance.
In order to improve her service, Molly is considering purchasing new dry-cleaning equipment, including a pressing machine that could substantially increase the speed at which she can dry-clean clothes and improve their appearance. The new machinery costs $16,200 installed and can clean 40 clothes items per hour (or 320 items per day). Molly estimates her variable costs to be $0.25 per item dry-cleaned, which will not change if she purchases the new equipment. Her current fixed costs are $1,700 per month. She charges customers $1.10 per clothing item.
a) What is Molly's current monthly volume?
b) If Molly purchases the new equipment, how many additional items will she have to dry-clean each month to break even?
c) Molly estimates that with the new equipment she can increase her volume to 4,300 items per month. What monthly profit would she realize with that level of business during the next 3 years? After 3 years?
d) Molly believes that if she doesn't buy the new equipment but lowers her price to $0.99 per item, she will increase her business volume. If she lowers her price, what will her new break-even volume be? If her price reduction results in a monthly volume of 3,800 items, what will her monthly profit be?
e) Molly estimates that if she purchases the new equipment and lowers her price to $0.99 per item, her volume will increase to about 4,700 units per month. Based on the local market, that is the largest volume she can realistically expect. What should Molly do?
2. The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.
a) Formulate a linear programming model for this problem.
b) Solve this model by using graphical analysis.
c) What would be the effect on the optimal solution if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?
3. The National Credit Union has $250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Credit union regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of defaults in such municipalities as Cleveland and New York, it is decided that no more than 40% of the investment be placed in bonds. How much should the National Credit Union invest in each security so as to maximize its return on investment?