A project involves laying 100 miles of oil distribution pipe in the Alaskan wilderness. It is desired to determine the lowest-cost crew size and composition that can get the job done within 90 days. Three different types of crew are available.

Each crew can work independently or work simultaneously with other crews. Crew 1 can lay pipes at the rate of 1 mile per day. If Crew 2 is to do the whole job alone, it can be finished in 120 days. Crew 3 can lay pipes at the rate of 1.7 miles per day, but this crew already has other imminent project commitments that will limit its participation in the piping project to only 35 contiguous days. All three crews are ready, willing, and available to accept their contracts at the beginning of the project. Crew 3 charges \(\$ 50,000 / \mathrm{mile}\) of pipe laid, Crew 2 charges \(\$ 35,000\) / mile, and Crew 1 charges \(\$ 40,000 /\) mile. Contracts can be awarded only in increments of 10 miles. That is, a crew can get a contract only for \(0,10,20,30\) miles, and so on. Required: Determine the best composition of the project crews and the minimum budget needed to finish the project in the shortest possible time.