2. A firm that manufactures souvenirs for tourists produces four different types of key chains. Each type of the keychain must be sliced, polished, and assembled and the time (in minutes) required for each of the processes are given as follows:

Type of Key Chain A. B. C. D

Slicing 3 2 3. 1 Polishing 1 1 1 1

Assembling 3. 2. 2 3

For a weekly production plan, the firm has available 100 labour hours of slicing time, 36 labour hours of polishing time, and 80 labour hours of assembling time for producing the key chains. The unit profits for each type of key chain (A, B, C, D) are $12, $10, $8, and $16 respectively. The firm has a contract with a retailer to supply at least 400 units of type B and at least 600 units of any combination of quantity for type A and C every week. From past experience, the firm can sell each week as many units of type A, B and C as it can produce, but only a maximum of 200 units of type D. Formulate the linear programming model algebraically for the above situation to determine the optimal number of each type of key chain to be produced each week to maximize the total profit (there is no need to find the optimal solution).