(Solved Homework): EXERCISES eeds to plan their onths. Honeydew Chemicals produces a single l. Honeydew…

EXERCISES eeds to plan their onths. Honeydew Chemicals produces a single l. Honeydew Chemicals Chief Operating Officer. Ash Molinaro, n production for the next three iid fertilner -for which the following relevant information for the next 3 periods (months) is available. PRODUCTION COST DEMAND INVENTORY HOLDING COST PRODUCTION CAPACITY PER LITER (SI CHARGED AT THE END OF A PERIODO PER LITER I 2.40 2.50 2.80 500 300 500 0.20 0.25 0.20 600 400 300 The company has an initial inventory of 100 liters at the beginning of period 1, and is required to hold a minimum inventory of at least 50 liters at the end of period 3. a. Formulate a linear program, clearly defining all variables used, to determine the production and inventory in each period that minimizes the total Honeydew over the 3 periods, while meeting its demand requirements. cost for b. Use Solver to find the optimal solution to the linear program from part a. Turn in the spreadsheet model with solution.

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EXERCISES eeds to plan their onths. Honeydew Chemicals produces a single l. Honeydew Chemical’s Chief Operating Officer. Ash Molinaro, n production for the next three iid fertilner -for which the following relevant information for the next 3 periods (months) is available. PRODUCTION COST DEMAND INVENTORY HOLDING COST PRODUCTION CAPACITY PER LITER (SI CHARGED AT THE END OF A PERIODO PER LITER I 2.40 2.50 2.80 500 300 500 0.20 0.25 0.20 600 400 300 The company has an initial inventory of 100 liters at the beginning of period 1, and is required to hold a minimum inventory of at least 50 liters at the end of period 3. a. Formulate a linear program, clearly defining all variables used, to determine the production and inventory in each period that minimizes the total Honeydew over the 3 periods, while meeting its demand requirements. cost for b. Use Solver to find the optimal solution to the linear program from part a. Turn in the spreadsheet model with solution.

Expert Answer

Answer
First let us define the LP to minimize the total cost of production
Minimum Cost = P1*C1+P2*C2+P3*C3+I1*c1+I2*c2+I3*c3
Here P1,P2,P3 are planned productions in Periods 1 , 2 & 3 respectively & C1,C2 & C3 are cost of productions in Periods 1,2 & 3 .
I1,I2 & I3 are closing inventories at the periods 1,2 & 3 and c1,c2&c3 are respective inventory holding costs .
Constraints are
P1<=600 , P2<=400 , P3<=300
I3=50
Now we have to solve using solver . Before going for solver let us analyze a few figures.
As per figures given total demand = 500+300+500 = 1300 units . So TD = 1300 units
As per figures given total capacity = 600+400+300=1300 . So TC =1300 units.
Further Opening Inventory = 100 units so OI=100 units
Closing Inventory = 50 units . So CI=50
So total planned production = TD-OI+CI = 1300-100+50=1250 units
So out of our capacity we have to make 50 units less in any of the periods .
Now using solver by putting formulas let us evaluate the total costs for 3 options where in we will make 50 units in each of these periods
Option 1
Period Planned Production
1 600
2 400
3 250
Period Production Cost $/Liter Demand Inventory Holding Cost $/liter on inventory at the end of the period Production Capacity Opening Inventory Planned Production Closing Inventory Cost of Production Inventory Holding Cost $ on inventory at the end of the period Total Cost
A B C D E F G=F+E-B H=A*G I=G*C J=H+I
1 2.4 500 0.2 600 100 600 200 1440 40 1480
2 2.5 300 0.25 400 200 400 300 1000 75 1075
3 2.8 500 0.2 300 300 250 50 700 10 710
Total Cost 3265
Option 2
Period Planned Production
1 550
2 400
3 300
Period Production Cost $/Liter Demand Inventory Holding Cost $/liter on inventory at the end of the period Production Capacity Opening Inventory Planned Production Closing Inventory Cost of Production Inventory Holding Cost $ on inventory at the end of the period Total Cost
A B C D E F G=F+E-B H=A*G I=G*C J=H+I
1 2.4 500 0.2 600 100 550 150 1320 30 1350
2 2.5 300 0.25 400 150 400 250 1000 62.5 1062.5
3 2.8 500 0.2 300 250 300 50 840 10 850
Total Cost 3262.5
Option 3
Period Planned Production
1 600
2 350
3 300
Period Production Cost $/Liter Demand Inventory Holding Cost $/liter on inventory at the end of the period Production Capacity Opening Inventory Planned Production Closing Inventory Cost of Production Inventory Holding Cost $ on inventory at the end of the period Total Cost
A B C D E F G=F+E-B H=A*G I=G*C J=H+I
1 2.4 500 0.2 600 100 600 200 1440 40 1480
2 2.5 300 0.25 400 200 350 250 875 62.5 937.5
3 2.8 500 0.2 300 250 300 50 840 10 850
Total Cost 3267.5
So the best option is Option 2 where we are making 550 units in Period 1 , 400 units in Period 2 and 300 units in Period 3.

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