Mission College Business Worksheet

User Generated

Naqenqn

Business Finance

Mission College

Description

Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:

From

To

Hamilton

Butler

Clermont

Southern Gas

10

20

15

Northwest Gas

12

15

18

Question : Assume that Southern Gas cannot provide any gas to Hamilton County. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs and solve it by excel

Unformatted Attachment Preview

Supplies 500 Problem #2 (a) 400 Southern Gas Northwest Gas - - Min 3 Constraints: - Constraints for supplies X₁ + X₁₂ + X₁3 ≤ 500 X₂₁ + X₂2 + X₂ 3 < 400 Хан 22 Constraints X₁₁ X₁2 + X₁₂ 40 24 + X₂1 = 400 = 200 22 15 for demand 18 Clermont 6) Decision variable: de 0 -Determine the plant that will minimize total distribution cost. Xij- amount of units shipped from plant (i) to three-county area (j) Obj function Hamitton X13 + X23 = 300 xij 200 i = 1, 2 / 3 = 1,2,3 c) Butle 10X₁₁ + 20X₁2+ 15X₁3 + 12X₂1 + 15X22 + 18X23 Domand 400 200 300 than -Southern - Hamilton amount 200 cost $2000 - Southern - Clermont amount 300, cost $ 4500 Northwest- Hamilton amount 200, cost $2400 Northwest-Butler amount 200, cost $3000. ⇒ Total cost is $ 44900.
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Explanation & Answer:
Worksheet
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Explanation & Answer

x12 + x13 <= 500 Southern supply capacityx21+ x22 + x23 <= 400 Northwest supply capacity x21 = 400 Hamilton demand forecastx12 + x22 = 200 Butler demand forecastx13 + x23 = 300 Clermont demand forecast

Obj.Function 𝑚𝑖𝑛 20𝑥12 + 15𝑥13 + 12𝑥21 + 15𝑥22 + 18𝑥23

Constraints

Supplies

x12...


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