) Suppose that a firm has $10 (thousand) dollars to invest on developing four products (P1, P2, P3, P4). The expected profits from each product depend on this initial investment (y) as follows:

P1: 25 + 5y for y>0

P2: 10 + 10y for y>0

P3: 50 + 3y for y>0

P4: 5 + 20y for y>0

If there is no investment in a product, then there will be no expected profit from that product. There are set amounts (all in thousands) that can be invested in each product: $1 or $2 for P1, $3 or $6 for P2, $4 or $5 for P3, and $2 or $3 for P4. Any other investment amounts are not allowed (although we can choose to invest $0 in any of the products). Use dynamic programming to determine the amount to invest in each product so that the total expected profit is maximized.