Question

A shipping freighter has space for two more shipping containers, but the combined weight cannot go over 20 tons. Four shipping containers are being considered. The following table provides details on the weight (in tons) and value of the contents of each container.

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Container	1	2	3	4
Weight of container (tons)	5	6	9	7
Value / Container	$6,000	$5,500	$7,500	$6,000

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Develop a binary integer model ( write all the constraints) that will determine the two containers, solve by SOLVER that will maximize the value of the shipment.

Answer 1

Formulating the problem

Decision variables

X1= Container 1 will be selected

X2= Container 2 will be selected

X3= Container 3 will be selected

X4= Container 4 will be selected

Constraints

X1, X2, X3, X4 = Binary variable {0.1}

X1+X2+X3+X4=2

5X1+6X2+9X3+7X4<=20

Objective function

Objective is to maximize total value of the shipment

MAX 6000X1+5500X2+7500X3+6000X4

We will now solve this problem using Solver as shown in screenshots below:

Optimal solution as per model is to choose Container 1 and Container 3 with maximum value of shipment is 13,500.

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