**quantatative analysis**

## Project Description:

1. classify the following problems as to whether they are pure-integer, mixed-integer, zero-one, goal, or nonlinear programming problems. work each problem on excel 2010 or windows qm and explain your answer for each problem.

maximize z = 5 x1 + 6 x1 x2 + 2 x2

subject to: 3 x1 + 2 x2 ≥ 6

x1 + x2 ≤ 8

x1, x2 ≥ 0

minimize z = 8 x1 + 6 x2

subject to: 4 x1 + 5 x2 ≥ 10

x1 + x2 ≤ 3

x1, x2 ≥ 0

x1, x2 = 0 or 1

maximize z = 10 x1 + 5 x2

subject to: 8 x1 + 10 x2 = 10

4 x1 + 6 x2 ≥ 5

x1, x2 integer

minimize z = 8 x12 + 4 x1 x2 + 12 x22

subject to: 6 x1 + x2 ≥ 50

x1 + x2 ≥ 40

2. a package express carrier is considering expanding the fleet of aircraft used to transport packages. of primary importance is that there is a total of $350 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. of secondary importance is that the company needs at least 10 new aircraft. it takes 150 hours per month to maintain the c1a, and 100 hours to maintain the c1b. the least level of importance is that there are a total of 1,200 hours of maintenance time available per month.

part 1: formulate this as an integer programming problem to maximize the number of pounds that may be carried. explain your answer.

part 2: rework the problem differently than in part 1 to suppose the company decides that what is most important to them is that they keep the ratio of c1bs to c1as in their fleet as close to 1.2 as possible to allow for flexibility in serving their routes. formulate the goal programming representation of this problem, with the other three goals having priorities p2, p3, and p4, respectively.

maximize z = 5 x1 + 6 x1 x2 + 2 x2

subject to: 3 x1 + 2 x2 ≥ 6

x1 + x2 ≤ 8

x1, x2 ≥ 0

minimize z = 8 x1 + 6 x2

subject to: 4 x1 + 5 x2 ≥ 10

x1 + x2 ≤ 3

x1, x2 ≥ 0

x1, x2 = 0 or 1

maximize z = 10 x1 + 5 x2

subject to: 8 x1 + 10 x2 = 10

4 x1 + 6 x2 ≥ 5

x1, x2 integer

minimize z = 8 x12 + 4 x1 x2 + 12 x22

subject to: 6 x1 + x2 ≥ 50

x1 + x2 ≥ 40

2. a package express carrier is considering expanding the fleet of aircraft used to transport packages. of primary importance is that there is a total of $350 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. of secondary importance is that the company needs at least 10 new aircraft. it takes 150 hours per month to maintain the c1a, and 100 hours to maintain the c1b. the least level of importance is that there are a total of 1,200 hours of maintenance time available per month.

part 1: formulate this as an integer programming problem to maximize the number of pounds that may be carried. explain your answer.

part 2: rework the problem differently than in part 1 to suppose the company decides that what is most important to them is that they keep the ratio of c1bs to c1as in their fleet as close to 1.2 as possible to allow for flexibility in serving their routes. formulate the goal programming representation of this problem, with the other three goals having priorities p2, p3, and p4, respectively.

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**Price Type:** Fixed

**Project Budget:**$10

**to**$30

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