A data-processing company processes three types of jobs - A, B, and C - for clients. In-house processing costs per job are estimated to be $1, $2, and $3 for job types A, B, and C, respectively.Each job requires two types of computing resources - CPU and storage. It requires:

1 unit of CPU, and 2 unit of storage to process each job of type A;

2 unit of CPU, and 2 units of storage to process each job of type B; and

2 unit of CPU, 3 units of storage to process each job of type C.

Over this time period it has 1,800,000 units of CPU, and 3,000,000 units of storage available.Because of contractual obligations the company must process 1,000,000 jobs of type A, 500,000 jobs of type B, and 600,000 jobs of type C in the upcoming week. Limited resource availability prevents the company from meeting the entire demands for all job types through in-house processing alone. The company may out-source some jobs to an external supplier. No in-house computing resources are used for out-sourced jobs. The external supplier charges $2 for each job of type A, $3 for each job of type B, and $4 for each job of type C.

What is the minimum cost attainable under an optimal plan?

How many jobs of each type should be processed in-house and out-sourced under this optimal plan?

How many units of CPU and storage are used up under this optimal plan?

The company has located an alternate business partner (New-Partner) that can only process jobs of type A. It can process at most 100,000 jobs of type A in the upcoming week, but the price per job is subject to negotiations. What is the maximum amount that the company should be willing to pay New-Partner for processing each unit of job type A? Justify your answer by explaining your approach.