Chapter 5 Problem 28

Homework 2

Chapter 5 Problem 28

Decision variables: 

xij =1 [if assign professor i to course j]

xij =0 [if not assign professor i to course j]

i= Strausbaygh (S), Kelley (K), Davidson (D), Merkle (M)

j= Statistics (1), Management (2), Finance (3), Economics (4)

Objectives:

Max [pic 1]

rij is the rating that professor i teaches course j

Constraints:

Professor nodes:

xS1+xS2+xS3+xS4=1

xK1+xK2+xK3+xK4 =1

xD1+xD2+xD3+xD4 =1

xM1+xM2+xM3+xM4 =1

Course nodes:

xS1+xK1+xD1+xM1=1

xS2+xK2+xD2+xM2=1

xS3+xK3+xD3+xM3=1

xS4+xK4+xD4+xM4=1

Solution:

Strausbaygh:  Economics

Kelley: Management,

Davidson: Finance,                

Merkle: Statistics

Optimal ratings: 310

Attach spreadsheet: (CH5_Q28)

Chapter 6 Problem 20

Decision variables: 

A= No. of item A to be shipped

B= No. of item B to be shipped

C= No. of item C to be shipped

D= No. of item D to be shipped

E= No. of item E to be shipped

F= No. of item F to be shipped

G= No. of item G to be shipped

Objectives:

Maximize value

Max 1800A+1400B+1100C+900D+1600E+1100F+1200G

Constraints:

1. Maximum capacity=2200,

700A+600B+450C+400D+650E+350F+600G <= 2200

1. At least 2 items of B,C and D,

B+C+D >= 2

1. If B is selected, G cannot be selected,

B+G <= 1

Nonnegative constraint,

 A, B, C, D, E, F, G = Integers

Solution:

Optimal decision:

A=0, B=0, C=0, D=2, E=0, F=4, G=0

Optimal objective value: 6200

Attach spreadsheet: CH6_Q20

Chapter 6 Problem 42

Decision variables: 

QA = No. of Product A

QB = No. of Product B

PA = Price of Product A: [(5500-QA)/200]

PB = Price of Product B: [(4500-QB)/225]

Objectives:

Maximize profit

Max [(PA-18) *QA] + [(PB-12) *QB]

Constraints:

1. Weekly production capacity for A=275: QA <= 275
2. Weekly production capacity for B=350: QB <= 350
3. 700 labor hours available: QA+2QB <= 700

Nonnegative constraint: QA and QB ≥ 0