Larry Edison is the director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 A.M. until midnight. Larry has monitored the usage of the center at various times of the day, and determined that the following number of computer consultants are required:

Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for 8 consecutive hours in any of the following shifts: morning (8 A.M.–4 P.M.), afternoon (noon–8 P.M.), and evening (4 P.M.–midnight). Full-time consultants are paid $14 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the above table. Part-time consultants are paid $12 per hour.
An additional requirement is that during every time period, there must be at least 2 full-time consultants on duty for every parttime consultant on duty.
Larry would like to determine how many full-time and how many part-time workers should work each shift to meet the above requirements at the minimum possible cost.

(a) Formulate a linear programming model for this problem.
C

(b) Solve this model by the simplex method.
3.4-11.* The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month’s production output. The table to the right shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be produced at each factory and the number of units ordered by each customer. (Go to the next column.)

Management now wants to determine the most economical plan for shipping the iron ore from the mines through the distribution network to the steel plant.

(a) Formulate a linear programming model for this problem.
C

(b) Solve this model by the simplex method.
A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer.

(a) Formulate a linear programming model for this problem.
C

(b) Solve this model by the simplex method.