Stats Solutions

[See Solution] The production manager of Koulder Refrigerators must decide how many refrigerators to produce in each of the next three months to meet demand

Question: The production manager of Koulder Refrigerators must decide how many refrigerators to produce in each of the next three months to meet demand at the lowest overall cost. There is a limited capacity in each month, and costs are expected to increase. If there are any items left in inventory at the end of a month, they incur a carrying cost. The relevant information is provided in the table below.

Month Capacity Demand Cost of production per unit Carrying cost per unit per month
1 130 100 $80 per unit $4.00
2 140 130 $90 per unit $4.50
3 170 160 $95 per unit $5.00

Management wants to have at least 15 units left at the end of month 3 to meet any unexpected demand at that time. The linear program and is shown below. Solve this on the computer and answer the questions that follow.

The variables are defined as:

X 1 = number of units produced in month 1 N 1 = number of units left at end of month 1
X 2 = number of units produced in month 2 N 2 = number of units left at end of month 2
X 3 = number of units produced in month 3 N 3 = number of units left at end of month 3

The linear program is:

Minimize cost = 80X 1 + 90X 2 + 95X 3 + 4N 1 + 4.5N 2 + 5N 3

X 1 < 130

X 2 < 140

X 3 < 170

X 1 = 100 + N 1

X 2 + N 1 = 130 + N 2

X 3 + N 2 = 160 + N 3

N 3 > 15

All variables > 0

Month Units produced Units remaining at end of month
1
2
3
Total cost =

Price: $2.99
Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document


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