ABC Beer is trying to devise a low cost supply chain for its brewing operation.
ID: 460415 • Letter: A
Question
ABC Beer is trying to devise a low cost supply chain for its brewing operation. Most of the ingredients are purchased from a local distributor, but ABC grows its own hops in 3 locations: Dublin, Milwaukee, and Redwood City. From these locations, the hops are sent to a processing plant in either Dallas or New York. After processing, the hops are sent to a brewery in one of three locations: Minneapolis, Toronto, or Santa Fe.
There are 80, 60, and 40 pounds of hops available at Dublin, Milwaukee, and Redwood City, respectively, and each of the breweries requires at least 50 pounds of hops, however, demand is sufficiently large so that there is no upper limit on the amount of hops that can be sent to any of the breweries. Each of the breweries will produce a different type of beer, and so the revenue per pound of hops is different at each of the breweries: Minneapolis generates $6 of revenue per pound of hops, Toronto generates $8 of revenue per pound of hops, and Santa Fe generates $12 of revenue per pound of hops. The per pound cost of shipping hops between the cities is given below. Formulate a linear program that can be used to determine how the hops should be routed through the supply chain in order to maximize the difference between revenue and shipping cost.
Ship. Cost per pound
Dublin
Milwaukee
Redwood City
Minneapolis
Toronto
Santa Fe
Dallas
4
2
2
3
3
1
New York
3
2
3
2
2
4
Ship. Cost per pound
Dublin
Milwaukee
Redwood City
Minneapolis
Toronto
Santa Fe
Dallas
4
2
2
3
3
1
New York
3
2
3
2
2
4
Explanation / Answer
Minimixe the cost:
z=80x1+ 60x2 + 40 x3
subject to the constraint
4x1+2x2+2x3<50
3x1+2x2+3x3<50
x1,x2x,x3>0
Maximize the revenue:
z=6x1+8x2+12x3
subject to the constraint
3x1+2x2<50
3x1+2x2<50
1x1+4x2<50
x1,x2>0
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