Question 81) A package express carrier is considering expanding the fle

81) A package express carrier is considering expanding the fleet of aircraft used to transport packages. There is a total of $220 million allocated for purchases. Two types of aircraft may be purchased – the C1A and the C1B. The C1A costs $25 million, while the C1B costs $18 million. The C1A can carry 60,000 pounds of packages, while the C1B can only carry 40,000 pounds of packages. The company needs at least eight new aircraft. In addition, the firm wishes to purchase at least twice as many C1Bs as C1As. Formulate this as an integer programming problem to maximize the number of pounds that may be carried.

82) Smalltime Investments Inc. is going to purchase new computers for most of the employees. There are ten employees, and at least eight computers must be purchased. The cost of the basic personal computer with monitor and disk drive is $2,000, while the deluxe version with VGA and advanced processor is $3,500. Due to internal politics, the number of deluxe computers must be no more than half the number of regular computers, but at least three deluxe computers must be purchased. The budget is $27,000. Formulate this as an integer programming problem to maximize the number of computers purchased.

83) Smalltime Investments Inc. is going to purchase new computers. There are ten employees, and the company would like one for each employee. The cost of the basic personal computer with monitor and disk drive is $2,000, while the deluxe version with VGA and advanced processor is $3,500. Due to internal politics, the number of deluxe computers should be less than half the number of regular computers, but at least three deluxe computers must be purchased. The budget is $27,000, although additional money could be used if it were deemed necessary. All of these are goals that the company has identified. Formulate this as a goal programming problem.

84) Allied Manufacturing has three factories located in Dallas, Houston, and New Orleans. They each produce the same product and ship to three regional warehouses: #1, #2, and #3. The cost of shipping one unit of each product to each of the three destinations is given below.

There is no way to meet the demand for each warehouse. Therefore, the company has decided to set the following goals: (1) the number shipped from each source should be as close to 100 units as possible (overtime may be used if necessary), (2) the number shipped to each destination should be as close to the demand as possible, (3) the total cost should be close to $1,400. Formulate this as a goal programming problem.

85) The Elastic Firm has two products coming on the market, Zigs and Zags. To make a Zig, the firm needs 10 units of product A and 15 units of product B. To make a Zag, they need 20 units of product A and 15 units of product B. There are only 2,000 units of product A and 3,000 units of product B available to the firm. The profit on a Zig is $4 and on a Zag it is $6. Management objectives in order of their priority are:

(1) Produce at least 40 Zags.

(2) Achieve a target profit of at least $750.

(3) Use all of the product A available.

(4) Use all of the product B available.

(5) Avoid the requirement for more product A.

Formulate this as a goal programming problem.

86) Data Equipment Inc. produces two models of a retail price scanner, a sophisticated model that can be networked to a central processing unit and a stand-alone model for small retailers. The major limitations of the manufacturing of these two products are labor and material capacities. The following table summarizes the usages and capacities associated with each product.

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