Graduate School of Business
Operations Management and Research Assignment
November 20, 2022
Instructions
Answer all questions
Submit in PDF (after computing on a word document)
DUE: November 20, 2022
Time Allowed: 3 hours
Question 1
John Mulyamuntu owns five parcels of farmland broken into a block 1, block 2, block 3, block 4 and block 5 sector. John is involved primarily in growing Millet, Soyabeans, and Maize crops and is currently preparing her production plan for next year. The Mulyamuntu and 10miles Water Company have signed off an annual contract for water allocation for 913 hectare-meter. Each parcel can only tolerate a specified amount of irrigation per growing season, as specified in the following table:
Parcel Area in Hectare Water Irrigation Limit (Hectare-Meters)
Block 1 809 395
Block 2 931 419
Block 3 243 99
Block 4 445 62
Block 5 202 74
Each of John Mulyamuntu’s crops needs a minimum amount of water per hectare, and there is a projected limit on sales of each crop. Crop data follow:
Crop Maximum Sales Water Needed per Hectare
Millet 1,100 bags 0.20
Soya Beans 18 tons 0.36
Maize 22 tons 0.43
Mulyamuntu’s best estimate is that she can sell wheat at a net profit of K200 per bag, Soya Beans at K4,000 per ton, and Maize at K5,000 per ton. One Hectare of land yields an average of 1.5 tons of Soya Beans and 2.2 tons of Maize. The Millet yield is approximately 50 bags per Hectare.
a. How many decision variables are involved in this problem?
b. Formulate Mulyamuntu’s production plan given the information provided? (40 Marks).
Question 2
University of Wakwesu is building a new set of hostels for students. The following table is provided information regarding the building with activities and durations provided.
Activity Preceded by Duration (Weeks)
Excavation 4
Foundation Excavation 2
Steel Frame Foundation 4
Brick Work Steel Frame 6
Game Basement Plumbing Foundation 1
Game Basement Floor Game Basement Plumbing 2
Initial Plumbing Game Basement Plumbing 3
Initial Wiring Steel Frame 2
Airconditioning Steel Frame 4
Plaster Initial Plumbing; Initial Wiring 10
Tiling Plaster 3
Kitchen Fixtures Tiling 1
Final Plumbing Tiling 2
Final Wood work Tiling 3
Complete Roofing Brick Work 2
Gutters and drain pipes Complete Roofing 1
Water Drains Foundation 1
Vanishing Final Wood work; Painting 2
Painting Final Plumbing; Kitchen Fixtures 3
Complete electrical work Painting 1
Grading Gutters and drain pipes; Water Drains 2
Walk Paths and Landscaping Grading 5
With aid of a network diagram, compute the following:
a. Early Start, Early Finish
b. Late start, Late Finish
c. Indicate the critical path
d. Calculate the project slack
(30 Marks)
Question 3
A company has three factories X, Y, and Z and four warehouses A, B, C, and D. It is required to schedule factory production and shipments from factories to warehouses in such a manner so as to minimize total cost of shipment and production. Unit variable manufacturing costs (UVMC) and factory capacities and warehouse requirements are given below:
From UVMC To warehouses
Factories. Rs. Uni t shipping costs in Rs. Capacity in units per month.
A B C D
X 10 0 1 1 2 75
Y 11 1 2 3 1 32
Z 12 4 3 3 6 67
Requirement: 65 24 16 15
a. Find the optimal production and transportation schedule using the Northwest Conner and Steeping Stone methods
(30 marks)
2
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