1. Product Mix A firm owns or employs 2 kinds of resources A and B (note that these two kinds of "resources" could refer to employees with two different sets of skills). In a day, we have 100 hours of resource A available (for example, 100 manhours of type A employees) and 10 hours of resource B available. In the short run, the firm is unable to change the resource availabilities (that is, increase or decrease the man hours available). The firm faces unlimited demand for three kinds of services it offers, namely Alpha, Beta and Gamma. The prices for these services are $1000, $5000 and $2000, respectively per customer. Providing the Alpha service to a customer requires using 1 hour of resource A and none of B. The Beta service requires 1 hour of B but none of A. The Gamma service requires 0.9 hours of A and 0.1 hours of B. Formulate a linear program to help decide how many Alpha, Beta and Gamma orders it should accept on a daily basis in order to maximize its revenues.