QUESTION ONE (10 MARKS)

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 atthe 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 (10 MARKS)

A manufacturer of high precision machined components produces two different types, Xand Y. In any given week, there are 4,000 man-hours of skilled labor available. EachcomponentXrequiresoneman-hourforitsproductionandeachcomponentYrequires2man-hours. The manufacturing plant has the capacity to produce a maximum of 2,250componentsof typeX each weekas wellas 1,750components of typeY. Each component X requires 2kg of plate. Each week there are 10,000 kg each of rod and plateavailable. The company supplies a car manufacturer with the unions that at least 1,500components will be produced each week in total. If the unit contribution for component Xis30 and for componentY is 40;

Required:

1. Generatethelinear programmingformulation oftheproblem.
2. How many of each type should be made in order to maximize the totalcontributionperweek? Whatisthemaximumcontribution?
3. Identifythe binding andnon-bindingconstraints.

Determinethe shadow priceof anyone of thebingingconstra