(Linear Programming) - Nkrumah Farms encompasses 900 acres, and is planning to grow groundnut, soybeans, corn, and wheat in the coming planting season. Fertilizer costs per acre are: Ghs 3 for groundnut, Ghc 5 for soybeans, Ghs 2 for corn, and Ghs 1 for wheat. Nkrumah Farms estimate that each acre of groundnut will require an average of 4 hours of labour per week, while soybeans will require an average of 5 hours of labor per week. Corn and wheat will each require an average of 2 hours per week. Based on past yields and current market prices, Nkrumah Farms estimate a profit of Ghs 1200 for each acre of groundnut, Ghs 3,000 for each acre of soybeans, Ghs 2,000 for each acre of corn, and Ghs 1,000 for each acre of wheat. Nkrumah Farms cannot afford to spend more than Ghs 3,000 on fertilizer. In addition, local labor regulations require Nkrumah Farms to utilize at least 2,200 hours of labour per week. Based on past demands, Nkrumah Farms would also want to ensure that the number of acres allocated to wheat exceeds half that of soybean, and also exceeds half that of corn. a. Formulate a linear program to help Nkrumah Farms allocate the available land to the four crops in a manner that maximizes total profits ( b. Solve Nkrumah Farm's Linear Program using Excel Solver and provide the sensitivity. c. How many acres are recommended to be allocated to each crop and what is the expected total profit from following the recommended allocations? ( d. What would be the expected total profit if Nkrumah Farms ignores the recommended allocations and allocates 100 acres to Groundnut? e. Explain the meaning of the shadow price of Ghs 1600 for the Acres of land constraint. f. What would happen to the recommended allocations were the profit per acre of Groundnut change from Ghs 1200 to Ghs 2100? g. How many hours of labour would Nkrumah Farms need above the minimum labour hours of 2200?
(Linear Programming) - Nkrumah Farms encompasses 900 acres, and is planning to grow groundnut, soybeans, corn, and wheat in the coming planting season. Fertilizer costs per acre are: Ghs 3 for groundnut, Ghc 5 for soybeans, Ghs 2 for corn, and Ghs 1 for wheat. Nkrumah Farms estimate that each acre of groundnut will require an average of 4 hours of labour per week, while soybeans will require an average of 5 hours of labor per week. Corn and wheat will each require an average of 2 hours per week. Based on past yields and current market prices, Nkrumah Farms estimate a profit of Ghs 1200 for each acre of groundnut, Ghs 3,000 for each acre of soybeans, Ghs 2,000 for each acre of corn, and Ghs 1,000 for each acre of wheat. Nkrumah Farms cannot afford to spend more than Ghs 3,000 on fertilizer. In addition, local labor regulations require Nkrumah Farms to utilize at least 2,200 hours of labour per week. Based on past demands, Nkrumah Farms would also want to ensure that the number of acres allocated to wheat exceeds half that of soybean, and also exceeds half that of corn. a. Formulate a linear program to help Nkrumah Farms allocate the available land to the four crops in a manner that maximizes total profits ( b. Solve Nkrumah Farm's Linear Program using Excel Solver and provide the sensitivity. c. How many acres are recommended to be allocated to each crop and what is the expected total profit from following the recommended allocations? ( d. What would be the expected total profit if Nkrumah Farms ignores the recommended allocations and allocates 100 acres to Groundnut? e. Explain the meaning of the shadow price of Ghs 1600 for the Acres of land constraint. f. What would happen to the recommended allocations were the profit per acre of Groundnut change from Ghs 1200 to Ghs 2100? g. How many hours of labour would Nkrumah Farms need above the minimum labour hours of 2200?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:(Linear Programming) -
Nkrumah Farms encompasses 900 acres, and is planning to grow groundnut, soybeans, corn, and
wheat in the coming planting season. Fertilizer costs per acre are: Ghs 3 for groundnut, Ghc 5 for
soybeans, Ghs 2 for corn, and Ghs 1 for wheat. Nkrumah Farms estimate that each acre of groundnut
will require an average of 4 hours of labour per week, while soybeans will require an average of 5
hours of labor per week. Corn and wheat will each require an average of 2 hours per week. Based on
past yields and current market prices, Nkrumah Farms estimate a profit of Ghs 1200 for each acre of
groundnut, Ghs 3,000 for each acre of soybeans, Ghs 2,000 for each acre of corn, and Ghs 1,000 for
each acre of wheat. Nkrumah Farms cannot afford to spend more than Ghs 3,000 on fertilizer. In
addition, local labor regulations require Nkrumah Farms to utilize at least 2,200 hours of labour per
week.
Based on past demands, Nkrumah Farms would also want to ensure that the number of acres
allocated to wheat exceeds half that of soybean, and also exceeds half that of corn.
a. Formulate a linear program to help Nkrumah Farms allocate the available land to the four crops in
a manner that maximizes total profits (
b. Solve Nkrumah Farm's Linear Program using Excel Solver and provide the sensitivity.
c. How many acres are recommended to be allocated to each crop and what is the expected total
profit from following the recommended allocations? (
d. What would be the expected total profit if Nkrumah Farms ignores the recommended allocations
and allocates 100 acres to Groundnut?
e. Explain the meaning of the shadow price of Ghs 1600 for the Acres of land constraint.
f. What would happen to the recommended allocations were the profit per acre of Groundnut change
from Ghs 1200 to Ghs 2100?
g. How many hours of labour would Nkrumah Farms need above the minimum labour hours of 2200?
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