Reference no: EM132757531

A company ABC hires you as a consultant to help them schedule their production. The company can only hire full time employees, who work 5 consecutive days in a week and take two days off. (For example, a consultant can work from Tuesday through Saturday and take Sunday and Monday off.) The salary for a full-time worker is $ 1400/week. There are 10 machines available in the factory. Each machine needs exactly one worker to operate. Each machine can produce at most 50 units of the products (wooden frames, for example) per day. The manager of ABC estimate the demand of the product in any day as the following table: (Max allowed to produce per day)

Qutantities of product Demand on daily basis for entire week:

Mon leq 200

Tue. leq 300

Wed. leq 250

Thursleq. 300

Fri. leq 200

Sat. leq 500

Sun. leq 400

The production cost of the product is $ 50/unit. The market price of the product is $ 150/unit. Because the space is extremely expensive in ABC, the manager decided to hold NO inventory. If a customer comes and there is no product available, the customer leaves forever. (That is, if the demand is 200 units on Monday and we only produce 180 units, only 180 units are sold.)

(a). Formulate linear constraints to maximize ABC's product per week. Define your decision variables, state and explain your objective and constraints clearly.

(b). Give a feasible solution to your model with the corresponding objective value.