Three plants-P1, P2, and P3-of a gas corporation supply gasoline to three of their distributors located in the city at three different locations-A, B, and C. The plants' daily capacities are 4500, 3000, and 5000, gallons, respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below.
?
Distributor
Plant
A
B
C
P1
0.8
0.5
1
P2
0.7
0.65
0.8
P3
0.5
0.45
0.7
?
Because of a failure of expected supply earlier, the distributors A, B, and C have decided to charge a penalty this time of $0.45, $0.55, and $0.5 per gallon, respectively, to avoid any further delays.Now, determine the optimum supply of gasoline to the distributors in order to minimize the total transportation cost as well as the charges payable as penalty.
What will be an ideal response?
x12: number of gallons of gasoline supplied from Plant 1 to Distributor B
.
.
.
x33: number of gallons of gasoline supplied from Plant 3 to Distributor C
?
Min 0.8x11 + 0.5x12 + 1x13 + 0.7x21 + 0.65x22 + 0.8x23 + 0.5x31 + 0.45x32 + 0.7x33
s.t.
x11 + x12 + x13? 4,500
x21 + x22 + x23? 3,000
x31 + x32 + x33? 5,000
x11 + x21 + x31 = 5,500
x12 + x22 + x32 = 2,500
x13 + x23 + x33 = 4,200
x11, x12, …, x33? 0
?
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