Table 1 Distance between refineries and distribution areas (pipeline miles) 2. T
ID: 386211 • Letter: T
Question
Table 1 Distance between refineries and distribution areas (pipeline miles) 2. The Willy Tonka Factory creates chooolate crunch bars and chocolate peantbutter bars During any month, the Factory can make at most 100 pounds of bars. The cost to produce a pound of chocolate bars and the demands for pounds of bars, which must be met on time, are listed in the table below. It costs 80.20 to hold a pound of chocolate crunch bars in inventory for one month and $0.10 to hold a pound of chocolate peanut bter bars in inventory for one month. Formulate an LP to minimize the total cost of meeting the next three months demands for chocolate bars Item Month 1 Month 2Month 3 (lb) 60 (1b) 50 20 (lb) Choc. Crunch Choc. Peanut 20 Item Month 1 Month 2 Month 3 (S/lb)(S/l (S/lb) 1.10 3.05 Choe. Crunch1.00 1.10 3.20 Choc. Peanut 3.0Explanation / Answer
Formula LP model as under:
Decision variables: Let C1, C2, C3 be the quantity (pounds) of Choc. Crunch bars to be produced in months 1,2,3 respectively
P1, P2, P3 be the quantity (pounds) of Choc. Peanut bars to be produced in months 1,2,3 respectively
VC1, VC2, VC3 be the ending inventory of Choc. Crunch bars in month 1,2,3 respectively
VP1, VP2, VP3 be the ending inventory of Choc. Peanut bars in month 1,2,3 respectively
Objective: Min Z = 4*C1+4.1*C2+4.1*C3+3*P1+3.05*P2+3.2*C3+0.2*(VC1+VC2+VC3)+0.1*(VP1+VP2+VP3)
Constraints:
C1-VC1 = 50
C2+VC1-VC2 = 60
C3+VC2-VC3 = 55
P1-VP1 = 20
P2+VP1-VP2 = 50
P3+VP2-VP3 = 20
C1+P1 <= 100
C2+P2 <= 100
C2+P3 <= 100
All variables >= 0
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