Reference no: EM133071867

QUESTION ONE - KCA University College of business chairperson of the department has the problem of providing lecturers for all the courses offered by his department at the highest possible level of education quality. He has got three professors and one Teaching Assistant (TA). Four course s must be offered and after appropriate introspection and evaluation he has arrived at the following relative ratings (100= best rating) regarding the ability of each instructor to teach each of the four courses, respectively

	Course 1	Course 2	Course 3	Course 4
Prof 1	70	50	70	80
Prof 2	30	70	60	80
Prof 3	30	40	50	70
TA	40	20	40	50

Required - How should he assign his staff to the courses to maximize educational quality in his department?

QUESTION TWO - A manufacturer of high precision machined components produces two different types, X and Y. In any given week, there are 4,000 man-hours of skilled labor available. Each component X requires one man-hour for its production and each componentY requires 2 man-hours. The manufacturing plant has the capacity to produce a maximum of 2,250 components of type X each week as wellas 1,750 components of type Y. Each component X requires 2kg of plate. Each week there are 10,000 kg each of rod and plate available. The company supplies a car manufacturer with the unions that at least 1,500 components will be produced each week in total. If the unit contribution for component X is £30 and for component Y is £40;

Required -

1. Generate the linear programming formulation of the problem.

2. How many of each type should be made in order to maximize the total contribution per week? What is the maximum contribution?

3. Identify the binding and non-binding constraints.