Question

A Ship has three spaces types for storing loads: North, south, and West. These spaces have capacity limits on both weight and space, as summarized below: Space type Weight capacity (Tons) North 12 South 18 West 15 capacity cubic feet 7000 8000 5000 The weight of the load in the space type must be the same proportion of that space weight capacity to maintain the balance of the ship. The following four Loads have been offered for shipment on an upcoming trip as space is available: Load Weight (Tons) Volume (cubic feet/Ton) Profit dollars/Ton 1 20 500 320 2 16 700 400 3 25 500 380 4 13 400 290 Any portion of these loads can be accepted. The objective is to determine how much (if any) of each load should be accepted and how to distribute each among the space type to maximize the total profit for the trip. (a) Formulate a linear programming model for this problem. (b) Solve this model by the simplex method to find one of its multiple optimal solution

          A Ship has three spaces types for storing loads: North, south, and West. These spaces have
capacity limits on both weight and space, as summarized below:
Space type
Weight capacity (Tons)
North
12
South
18
West
15
capacity cubic
feet
7000
8000
5000
The weight of the load in the space type must be the same proportion of that space weight
capacity to maintain the balance of the ship. The following four Loads have been offered for
shipment on an upcoming trip as space is available:
Load
Weight
(Tons)
Volume (cubic
feet/Ton)
Profit
dollars/Ton
1
20
500
320
2
16
700
400
3
25
500
380
4
13
400
290
Any portion of these loads can be accepted. The objective is to determine how much (if any) of
each load should be accepted and how to distribute each among the space type to maximize the
total profit for the trip.
(a) Formulate a linear programming model for this problem.
(b) Solve this model by the simplex method to find one of its multiple optimal solution

A Ship has three spaces types for storing loads: North, south, and West. These spaces have
capacity limits on both weight and space, as summarized below:
Space type
Weight capacity (Tons)
North
12
South
18
West
15
capacity cubic
feet
7000
8000
5000
The weight of the load in the space type must be the same proportion of that space weight
capacity to maintain the balance of the ship. The following four Loads have been offered for
shipment on an upcoming trip as space is available:
Load
Weight
(Tons)
Volume (cubic
feet/Ton)
Profit
dollars/Ton
1
20
500
320
2
16
700
400
3
25
500
380
4
13
400
290
Any portion of these loads can be accepted. The objective is to determine how much (if any) of
each load should be accepted and how to distribute each among the space type to maximize the
total profit for the trip.
(a) Formulate a linear programming model for this problem.
(b) Solve this model by the simplex method to find one of its multiple optimal solution

Added by Susan W.

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