he ABC Company is producing one product. The forecast for the demand in the next
ID: 364072 • Letter: H
Question
he ABC Company is producing one product. The forecast for the demand in the next 6 months is given in the table below:
Month
1
2
3
4
5
6
Demand (units)
1,200
2,200
2,400
1,600
1,200
1,000
Units can be produced during regular-time and during over-time. The cost of producing a unit during regular time is $40 and the cost to produce a unit during over time is $60. There are 1,000 hours of regular time and 500 hours of overtime available each month. The cost of storing one unit in inventory from one month to the next is $8. The maximum capacity of the storage is 2,500 units.
The production manager is developing a linear program to determine a minimum cost 6-months production plan which takes into account production and inventory costs. He defines the following decision variables:
Ri = the number of units produced in month i during Regular Time (i=1,2,….,6)
Vi= the number of units produced in month i during Over Time (i=1,2,….,6)
Si= the number of units held in inventory at the end of month i (i=1,2,….,6)
Which of the following equations represents the ‘balance constraint’ for month 3? (i.e. establishing the relationship between production, demand, and inventory levels during month 3)
R3 + V3 +S3 = 2400
40 R3 + 60 V3 +8 S3 = 2400
S2 + R3 + V3 – S3 = 2400
S3 + R3 + V3 – S2 = 2400
None of the above
he ABC Company is producing one product. The forecast for the demand in the next 6 months is given in the table below:
Month
1
2
3
4
5
6
Demand (units)
1,200
2,200
2,400
1,600
1,200
1,000
Units can be produced during regular-time and during over-time. The cost of producing a unit during regular time is $40 and the cost to produce a unit during over time is $60. There are 1,000 hours of regular time and 500 hours of overtime available each month. The cost of storing one unit in inventory from one month to the next is $8. The maximum capacity of the storage is 2,500 units.
The production manager is developing a linear program to determine a minimum cost 6-months production plan which takes into account production and inventory costs. He defines the following decision variables:
Ri = the number of units produced in month i during Regular Time (i=1,2,….,6)
Vi= the number of units produced in month i during Over Time (i=1,2,….,6)
Si= the number of units held in inventory at the end of month i (i=1,2,….,6)
Which of the following equations represents the ‘balance constraint’ for month 3? (i.e. establishing the relationship between production, demand, and inventory levels during month 3)
Answers: a.R3 + V3 +S3 = 2400
b.40 R3 + 60 V3 +8 S3 = 2400
c.S2 + R3 + V3 – S3 = 2400
d.S3 + R3 + V3 – S2 = 2400
e.None of the above
Explanation / Answer
HI,
Thanks for the question.
Since the R3 will be the units that is produced in the regular time of month 3, V3 will be the units that is produced in the overtime of month 3 and S3 will be the units that is left in the inventory at the end of month 3, The balance can be calculated as:
The total item that are fulfilled in that month will be the total items that are in the inventory (S2) plus the total items produced (R3 + V3) minus the items left in the inventory (S3). This should be equal to the demand for the month.
The equation will be as follows:
S2 + R3 + V3 - S3 = 2400
So the right option is option C
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