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GROUP ASSIGNMENT

Student Guidelines 1. Each group consist of 5 person per group. Ideally to have mixtures of gender and ethnics in a group. 2. Each group required to learn Linear Programming using Microsoft Excel’s Solver. You may refer to Business Mathematics reference books, video at Youtube or website. 3. Solve the Linear Programming questions using Microsoft Excel’s Solver. You need to print screen each step for each questions and state conclusion. 4. Produce educational video(s) to explain the solution for some questions. You may decide which questions to be recorded. 5. Please submit your assignment in bound. 6. Plagiarism, copying and cheating will NOT be awarded any mark, and disciplinary actions will be taken instead. Any requires/ questions/ problems regarding this assignment should be directed to your lecturer either during lecture or in the consultation hours. 7. The due date to submit this assignment is on 13 November 2015.

Solve the following questions using Microsoft Excel’s Solver. Pick any of the questions and record/take video step by step on how to solve it using Microsoft Excel’s Solver.

1. Minimize C=2x-3y-4z

Subject to

-x+2y-z≤8

x-2y+2z≤10

2x+4y-3z≤12

x≥0, y≥0,z≥0

2. Minimize C=2x+3y

Subject to

8x+y≥80

3x+2y+2z≥100 x+4y≥80 x≥0, y≥0

3. Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type A vessel has 60 deluxe cabins and 160 standard cabins, whereas a type B vessel has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15-day cruise in May. It costs RM 44,000 to operate a type A vessel and RM 54, 000 to operate a type B vessel for that period. How many of each type vessel should be used to keep the operating costs to a minimum? What is the minimum cost?

4. Everest Deluxe World Travel has decided to advertise in the Sunday editions of two major newspaper in town. These advertisements are directed at the three groups of potential customers. Each advertisements in Newspaper I is seen by 70000 Group A customers, 40 000 Group B customers, and 20 000 Group C customers. Each advertisements in Newspaper II is seen by 10000 Group A customers, 20 000 Group B customers, and 40 000 Group C customers. Each advertisement in Newspaper I costs RM 1000, and each advertisement in Newspaper II costs RM 800. Everest would like their advertisement to be read by at least 2 million people from Group A, 1.4 million people from Group B, and 1 million people from Group C. How many advertisements should Everest place in each newspaper to achieve its advertising goals at a minimum cost? What is the minimum cost?

5. The owner of the Health Juice Bar wishes to prepare a low-calorie fruit juice with a high vitamin A and vitamin C content by blending orange juice and pink grapefruit juice. Each glass of the blended juice is to contain at least 1200 International Units (IU) of vitamin A and 200 IU of vitamin C. One ounce of orange juice contains 60 IU of vitamin A, 16 IU of vitamin C, and 14 calories; each ounce of pink grapefruit juice contains 120 IU of vitamin A, 12 IU of vitamin C, and 11 calories. How many ounces of each juice should a glass of the blend contains if it is meet the minimum vitamin requirements while containing a minimum number of calories?

6. Maximize P=6x+5y+4z

Subject to

2x+y+z≤180

x+3y+2z≤300

2x+y+2z≤240

x≥0, y≥0,z≥0 7. Maximize P=x+y+2z+3w

Subject to

3x+6y+4z+2w≤12

x+4y+8z+4w≤16

2x+y+4z+w≤10

x≥0, y≥0,z≥0, w≥0

8. National Business Machines Corporation manufactures two models of fax machines: A and B. Each model A costs RM 100 to make, and each model B costs RM 150. The profits are RM 30 for each model A and RM 40 for each model B fax machines. If the total number of fax machines demanded each month does not exceed 2500 and the company has earmarked no more than RM 600,000/month for manufacturing costs, find how many units of each model National should make each month to maximize its monthly profit. What is the largest monthly profit the company can make?

9. Ashley has earmarked at most RM 250,000 for investment in three mutual funds: a money market fund, an international equity fund, and a growth-and-income fund. The money market fund has a rate of return of 6%/year, the international equity fund has a rate of return of 10%/year, and the growth-and-income fund has a rate of return of 15%/year. Ashley has stipulated that no more than 25% of her total portfolio should be in the growth-and –income fund and that no more than 50% of her total portfolio should be in the international equity fund. To maximize the return on her investment, how much should Ashley invest in each type of fund? What is the maximum return?

10. A company manufactures Product A, B and C. Each product is processed in three department: I,II, and III. The total available labor hours per week for Departments I, II and III are 900, 1080, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product as follows:

| Product A | Product B | Product C | Department I | 2 | 1 | 2 | Department II | 3 | 1 | 2 | Department III | 2 | 2 | 1 | Profit | RM 18 | RM 12 | RM 15 |

How many units of each product should the company produce to maximize its profit? What is the largest profit the company can realize? Are there any resources left over?

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