Question

Four shipping containers can altogether take a maximum of 20 tons for one shipment order. The following table provides details on the weight (in tons) and value of each container:

Container	1	2	3	4
Weight of container (tons)	5	6	9	7
Value / Container	$6000	$5500	$7500	$6000

Develop a binary integer model that will determine the two containers and the quantity that should be considered for shipment using these two containers (2 out of 4 containers) to maximize the value of the shipment.

Answer 1

LP Formulation

Objective Function -

Maximize Value Z = 6000X1+5500X2+7500X3+6000X4

s.t. constraints -

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

X1+X2+X3+X4 = 2

X_i = 0 or 1

Maximum value is 13500 from the below solver solution

Objective Function - Maximize Value Z = 6000X1 + 5500X2 + 7500X3 + 6000X4 s.t. constraints - 5X1 + 6X2 + 9X3 + 7X3 < = 20 X1 + X2 + X3 + X4 = 2 X_i = 0 or 1 Maximum value is 13500 from the below solver solution \r\n Solving method Select the GRG Nonlinear engine for Solver Problem that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problem that non-smooth.