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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 (x) as follows:
P1: 40 + 10x for x>0
P2: 10 + 40x for x>0
P3: 50 + 5x for x>0
P4: 5 + 50x for x>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: $2 or $6 for P1, $2 or $4 for P2, $3 or $5 for P3, and $1 or $3 for P4. Any other investment amounts are not allowed (although we can choose to invest $0 in any of the products). For example, the only amounts allowed for Use dynamic programming to determine the amount to invest in each product so that the total expected profit is maximized.
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