Question

Advance Engineering Corporation (AEC) provides paving and bridge maintenance services. Paving requires 7 hour of labor and 2 tons of material, and bridge maintenance requires 2 hour of labor and 12 tons of material. Currently, 28 hours of labor and 24 tons of material are available. Each Paving contract contributes $50 to profit, and each Bridge Contract contributes $100 to profit. Formulate and solve an integer programing problem to maximize AEC’s profit. (Please solve using branch and bound method)

Answer 1

Decision Variables:

Let,

The number of paving contracts = x1

Number of Bridge Contract = x2

Objective Function:

Here we have to maximize the profit

Profit from a paving contract = $50

Profit from a Bridge maintenance Contract = $100

MAX 50*x1 + 100*x2

Constraints:

We cant use labor or materials more than availability.

Paving requires 7 hour of labor and 2 tons of material, and bridge maintenance requires 2 hour of labor and 12 tons of material.

Available labor = 28 hours

Available material = 24 tons

7*x1 + 2*x2 <= 28

2*x1 + 12*x2 <= 24

Number of paving and bridge maintenance cant be negative.

x1, x2 >= 0

A contract must be completed (and hence not fractional)

x1, x2 = integer

Putting in Excel:

Solver Parameters:

Optimal Solution:

Number of Paving = 3

Number of Bridge Maintenance = 1

Profit = $250

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