A local asset management oversees the repair and replacement of the highway infr

Question

A local asset management oversees the repair and replacement of the highway infrastructure system. The annual budget allocations are: $50,000,000 for urban assets, $20,000,000 for suburban assets, and $10,000,000 for rural assets. Assets can be upgraded to satisfy GASB 34 requirements either by repair or replacement. The repair related costs are $200,000, $125,000, and $80,000 per linear-mile of urban, suburban, and rural roads, respectively. The replacement costs are $1,500,000, $1,100,000, and $750,000 per linear-mile of urban, suburban, and rural roads, respectively. You are required to replace at least 5 linear-mile of roads and repair at least 15 miles of roads. Each linear-mile of new road is credited with 10 year of service life, and each linear-mile of repaired road is credited with 2.5 years of service life. There are currently 200 miles of roads and 40 percent are in need of repair.

For undergraduate students, your task is to formulate the above problem as a Linear Program (LP) but do not solve for solution.

For graduate students, your task is to formulate the above problem as a Linear Program (LP) and solve for solution using Excel or other preferred methods. You must copy and paste your solution worksheet to receive credit

Explanation / Answer

Annual budget:

$ 50,000,000 for urban assets.

$20,000,000 for suburban assets.

$ 10,000,000 for rural assets.

Repair related cost:

$ 200,000/linear mile for urban

$ 125,000/linear mile for suburban

$ 80,000/linear mile for rural

replacement cost

$1,500,000/linear mile for urban

$ 1,100,000/linear mile for suburban

$ 750,000/linear mile for rural

replace atleat 5 linear mile of roads and repair atleat1 5 linear mile of roads.

credited new road with 10 year of service life and repair road is credited 2.5 yr.

200 miles of road and 40% is need of repair=80 roads

let variable X1 for repair and X2 for peplacement miles.

therefor lpp,

Objective Function:

to maximise the credit

maximize=2.5X1+10X2

Subject to Constrain,

200,000X1+1,500,000X2 <=50,000,000 for urban

125,000X1+1,100,000X2 <=20,000,000 for suburban

80,000X1+750,000X2 <=10,000,000 for rural

X1>= 15

X2>= 5

X1+X2= 80 need to repair

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