MS5220 Management Science HW5 Assignment

MS5220 Management Science HW5 Assignment

Q1.
#43 the trim loss problem

The Cach and Carry Building Supply Compny has received the following order for boards in three lengths:

Length Order (quantity )
7 ft. 700
9 ft. 1200
10 ft. 300

The company has 25-foot stadard-length boards in stock. Therefore, the standard-length boards must be cut into the lengths necessary to met order requirements.

Naturally, the company wishes to MINIMIZE the number of standard-length boards used. The company must therefore determine HOW TO cut up the 25-foot boards to meet the order requirements and minimize the number of standard-length boards used.

a) Formulate a linear programming model for this problem.
b) solve the model by using the computer.
c) When a board is cut in a specific pattern, the amount of board left over is referred to as " trim loss".

Reformulate the linear programming model for this problem, assuming that the objective is to minimize trim loss than to minimize the total number of boards used, and solve this model. How does this affect the solution.


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Q2 #38

Dr. Maureen Becker, the head administratorat EE hospital, must determine a schedule for nurses to make sure there are enough of them ON DUTY throughout the day.
during the day, the demand for nurses varies. During the day, the demand for nurses varies.

Maureen has broken the day into twelve 2-hour periods (2 X 12 =24 ).

i) The slowest time of th day encompasses the three periods ( 3 X 2 =6 ) from 12:00 a.m. to 6:00 a.m., which beginning at midnight, require a minumum of 30, 20, and 40 nurses, respectively.

ii) The demand for nurses steadily increases during the next four daytime periods (4 X 2 = 8). Beginning with the 6:00 am-8:00 am period, a minimum of 50, 60,80 and 80 nurses are required for these four periods respectively.

iii) After 2:00 p.m. the demand for nurses DECREASES during the afternoon and evening hours.

iv) For the five 2-hour periods ( 5 X 2 = 10 ) beginning at 2:00pm and endng at midnight, 70,70,60,50, and 50 nurses are required, respectively.

A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours.

Dr. Becker wants to determine a nursing schedule that will meet the hospital's MINIMUM requirement throughout the day while using the minimum number of nurses.

a) Formulate a linear programming model for this problem.
b) Solve this model by using the computer.