General Tso’s Generators must decide how many generators to produce in each of t
ID: 3339054 • Letter: G
Question
General Tso’s Generators must decide how many generators to produce in each of the next four months to meet demand at the lowest overall cost. There is a limited capacity in each month, and costs are expected to increase. The relevant information is provided in the table below.
Month
Capacity
Demand
Cost of production
1
150
120
$80 per unit
2
150
130
$80 per unit
3
160
170
$85 per unit
4
160
140
$85 per unit
Each item that is produced in a month but carried over to the next month incurs a carrying cost equal to 10% of the unit cost in that month. Thus, anything left in inventory at the end of month 1 incurs an $8 (10% of $80) cost to be carried over to the next month. Management wants to have at least 10 units left at the end of month 4 to meet any unexpected demand at that time. Linear programming was used to help with this. The variables are defined as:
Xi = number of units produced in month i, for i = 1, 2, 3, 4.
(e.g. X2 = number of units produced in month 2)
Nj = number of units left at end of month j, for j = 1, 2, 3, 4.
The linear program is:
Minimize cost = 80X1 + 80X2 + 85X3 + 85X4 + 8N1 + 8N2 + 8.5N3 + 8.5N4
Subject to:
X1 < 150
X2 < 150
X3 < 160
X4 < 160
X1 = 120 + N1
X2 + N1 = 130 + N2
X3 + N2 = 170 + N3
X4 + N3 = 140 + N4
N4 > 10
All variables > 0
Use computer software to find the optimal solution and put answers in the table.
Note: For a discussion of constraints similar to constraints 5-8, see the production scheduling example in Chapter 8. When entering these into the computer, all variables should be on the left hand side of the inequality. For example, a constraint such as X1 = 120 + N1 would be written as X1 - N1 = 120.
Answer Sheet:
Month
Number produced
Number remaining at end of month
1
2
3
4
Total cost
Month
Capacity
Demand
Cost of production
1
150
120
$80 per unit
2
150
130
$80 per unit
3
160
170
$85 per unit
4
160
140
$85 per unit
Explanation / Answer
Month
Number produced
Number remaining at end of month
1
150
30
2
150
50
3
160
40
4
160
60
Total cost
52690
Month
Number produced
Number remaining at end of month
1
150
30
2
150
50
3
160
40
4
160
60
Total cost
52690
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