A small generator burns two types of fuel – low sulfur and high sulfur – to produce electricity. For one hour, each gallon of low sulfur emits 3 units of sulfur dioxide, generates 4 kilowatts electricity, and cost P600. Each gallon of high sulfur emits 5 units of sulfur dioxide, generates 4 kilowatts, and costs P500. The Environmental Protection Agency insists that the maximum amount of sulfur dioxide that can be emitted per hour is 15 units. Suppose that at least 16 kilowatts must be generated per hour, how many gallons of low sulfur and how many gallons of high sulfur must be utilized per hour to minimize the cost of fuel?   Objective: minimize

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Instruction: Answer the following systematically. Strictly follow the format of the solution (Example problem + complete solution is provided in the photos below). I WON'T LIKE YOUR ANSWER IF IT IS NOT PROPERLY FOLLOWED AND INCORRECT)

A small generator burns two types of fuel – low sulfur and high sulfur – to produce electricity. For one hour, each gallon of low sulfur emits 3 units of sulfur dioxide, generates 4 kilowatts electricity, and cost P600. Each gallon of high sulfur emits 5 units of sulfur dioxide, generates 4 kilowatts, and costs P500. The Environmental Protection Agency insists that the maximum amount of sulfur dioxide that can be emitted per hour is 15 units. Suppose that at least 16 kilowatts must be generated per hour, how many gallons of low sulfur and how many gallons of high sulfur must be utilized per hour to minimize the cost of fuel?

 

Objective: minimize

 

EXAMPLE PROBLEM + SOLUTION
(PLEASE FOLLOW THE FORMAT OF HOW TO SOLVE PROPERLY)
Four foods X, X, X , and X, are to be purchased. X, contains 2 calories, no vitamin and costs
1"2'
P40 per piece. X, contains no calorie, 2 units of vitamin and costs Pl00 per piece. X, contains 1
unit of calorie, 1 unit of vitamin and costs P120 per piece. X, contains 3 units of calories, 2 units
of vitamins and costs P150 per piece. The minimum calories required is 18 units and the
minimum amount of vitamins is 8 units. How much of each food must be purchased to satisfy the
calorie and vitamin requirements to minimze the cost?
C = 40x, + 100x, + 120x, + 150x,
2x, + x, + 3x, 2 18
2x, + x, + 2x, 2 8
Minimize:
Subject to:
*, 2
C= 40x, + 100x, + 120x, + 150x, + 0s, + os, + 1000A, + 1000A,
2x, + x, + 3x, - S, + A, = 18
2x, + x, + 2x, - S, + A, = 8
Minimize:
Subject to:
+ A = 8
*, S, A 2 0
Table 1.
40
100
120
150
1000
1000
Var
Qty
X2
A,
A,
1000
A,
18
3
-1
1000
A,
2
-1
26000 2000
5000 -1000 -1000
1000
2000
2000
1000
z,
-1960
-1900
-1880
4850
1000
1000
2.
2.
Transcribed Image Text:EXAMPLE PROBLEM + SOLUTION (PLEASE FOLLOW THE FORMAT OF HOW TO SOLVE PROPERLY) Four foods X, X, X , and X, are to be purchased. X, contains 2 calories, no vitamin and costs 1"2' P40 per piece. X, contains no calorie, 2 units of vitamin and costs Pl00 per piece. X, contains 1 unit of calorie, 1 unit of vitamin and costs P120 per piece. X, contains 3 units of calories, 2 units of vitamins and costs P150 per piece. The minimum calories required is 18 units and the minimum amount of vitamins is 8 units. How much of each food must be purchased to satisfy the calorie and vitamin requirements to minimze the cost? C = 40x, + 100x, + 120x, + 150x, 2x, + x, + 3x, 2 18 2x, + x, + 2x, 2 8 Minimize: Subject to: *, 2 C= 40x, + 100x, + 120x, + 150x, + 0s, + os, + 1000A, + 1000A, 2x, + x, + 3x, - S, + A, = 18 2x, + x, + 2x, - S, + A, = 8 Minimize: Subject to: + A = 8 *, S, A 2 0 Table 1. 40 100 120 150 1000 1000 Var Qty X2 A, A, 1000 A, 18 3 -1 1000 A, 2 -1 26000 2000 5000 -1000 -1000 1000 2000 2000 1000 z, -1960 -1900 -1880 4850 1000 1000 2. 2.
Table 2.
C,
40
100
120
150
1000
1000
Var
Qty
A,
Az
1000
-3
-1/2
-1
3/2
-3/2
150
4
1/2
-1/2
1/2
z,
2000
150
1000
6600
-2850
-425
-1000
1425
-1425
C, - Z,
-1960
2950
545
1000
-1425
2425
Table 3.
40
100
120
150
1000
1000
Var
Qty
40
-3/2
-1/4
-1/2
3/4
1/2
-3/4
150
1/2
-1/2
1/2
720
40
90
65
150
-20
45
20
45
z,
10
55
20
45
80
955
'z -'5
Decision:
Food X, = 3,
Food X, = 0,
Food X, = 0,
Food X, = 4,
Minimum Cost of P720.
Transcribed Image Text:Table 2. C, 40 100 120 150 1000 1000 Var Qty A, Az 1000 -3 -1/2 -1 3/2 -3/2 150 4 1/2 -1/2 1/2 z, 2000 150 1000 6600 -2850 -425 -1000 1425 -1425 C, - Z, -1960 2950 545 1000 -1425 2425 Table 3. 40 100 120 150 1000 1000 Var Qty 40 -3/2 -1/4 -1/2 3/4 1/2 -3/4 150 1/2 -1/2 1/2 720 40 90 65 150 -20 45 20 45 z, 10 55 20 45 80 955 'z -'5 Decision: Food X, = 3, Food X, = 0, Food X, = 0, Food X, = 4, Minimum Cost of P720.
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