Given

100,000 square yards of highway pavements. The network is in poor condition. It can be in one of three conditions: 1-good, 2-fair, and 3-poor.

The budget available will be $75,000 per period. All links are currently in condition 2. The interest rate is assumed to be 3%

1. Solve the above LP by using MATLAB or Excel to optimize cost.

2. Develop in the short-term solution to the pavement management problem that is needed to gradually reach the steady state solution. Formulate and solve this problem as a LP.

Table 1a: M&R costs ($/sq. yd.) Condition state Do nothing Routine mntce 5.0 10.0 15.0 Resurfacing 20.0 20.0 20.0 0 Table 1b: User costs ($/sq. yd.) Condition state User Costs 10 30 Table 2: Transition probability matrices 2a: Do Nothing state a t+1 state t 0.5 0.5 0 0.5 0.5 0 2b: Routine Maintenance state a t+1 state @ t 0.8 0.2 0.8 0 0.2 2c: Resurfacing state t+1 state a t 0.8 0.6 0.2 0.4 Table 1a: M&R costs ($/sq. yd.) Condition state Do nothing Routine mntce 5.0 10.0 15.0 Resurfacing 20.0 20.0 20.0 0 Table 1b: User costs ($/sq. yd.) Condition state User Costs 10 30 Table 2: Transition probability matrices 2a: Do Nothing state a t+1 state t 0.5 0.5 0 0.5 0.5 0 2b: Routine Maintenance state a t+1 state @ t 0.8 0.2 0.8 0 0.2 2c: Resurfacing state t+1 state a t 0.8 0.6 0.2 0.4