Develop a linear program, Mathematics

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The production manager of Koulder Refrigerators must decide how many refrigerators 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 although this will increase in month 3.  Due to a new contract, costs are expected to increase.  The relevant information is provided in the table below.

Month

Capacity

Demand

Cost of production

1

140

110

$80 per unit

2

140

150

$85 per unit

3

160

130

$90 per unit

4

160

140

$95 per unit

Each item that is left at the end of the month and carried over to the next month incurs a carrying cost equal to 10% of the unit cost in that month (e.g. anything left in inventory at the end of month one incurs an $8 cost). Management wants to have at least 30 units left at the end of month four to meet any unexpected demand at that time. A linear program has been developed to help with this. However, this may or may not be totally correct. You should verify that it is the correct formulation before solving the problem. If it is not correct, make any necessary changes to the linear program before solving it on the computer.

X1 = number of units produced in month 1;  X2 = number of units produced in month 2; 

X3 = number of units produced in month 3; X4 = number of units produced in month 4;

N1 = number of units left at end of month 1; N2 = number of units left at end of month 2;

N3 = number of units left at end of month 3; N4 = number of units left at end of month 4

Minimize cost = 80X1 + 85X2 + 90X3 + 95X4+ 8N1 + 8.5N2 + 9N3+ 9.5N34

X1< 140

X2< 140

X3< 160

X4< 160

X1 = 110 + N1

X2 + N1 = 150 + N2

X3 + N2 = 130 + N3

X4 + N3 = 140 + N4

N4>30

All variables > 0


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