A local manufacturing firm produces four different metal products, each of which must be machined, polished, and assembled. The specific time requirements for each product are as follows:
Machining hours Polishing hours Assembling hours Unit profit $
Product 1 3 1 2 6
Product 2 2 1 1 4
Product 3 2 2 2 6
Product 4 4 3 1 8

Every week, the firm has available to it a total of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time.

The firm has a contract with a distributor to provide 50 units of Product 1, and 100 units of any combination of Products 2 and 3 every week.

Through other customers, the firm can sell any number of units of Products 1, 2, and 3. However, no more than 25 units of Product 4 can be sold in a week.

How many units of each product should the firm produce each week, so that it can meet its contractual obligations, and maximize its total profit?