Question: Consider the following bin packing problem. You have four items with size 4, 4, 5, 7 and the capacity ofeach bin is 10. The goal

Consider the following bin packing problem. You have four items with size 4, 4, 5, 7 and the capacity ofeach bin is 10. The goal is to find a packing plan that uses the least number of bins to contain all items.

1. Formulate an integer program to find the optimal bin packing plan.

2. Solve the LP-relaxation of the problem (i.e., set all variable as continuous variables) by Simplex method.Is there integrality gap in this problem?

Hint: the integrality gap means that you need more bins in any integer program than the LP-relaxation.

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