Egan, S_MGMT 651_hw3.pdf - Running head: HOMEWORK 3 MGMT...

Running head: HOMEWORK 3
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MGMT 651 – Homework 3
Stephanie Egan
University of Redlands
School of Business

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1. (15 points) Chapter 4 Problem 1.
Radio ads must not exceed 50% of total ads
3 variables – TV, newspaper, radio
r < .5 (t + r + n)
r < .5t + .5r + .5n
-.5t + .5r - .5n < 0
TV ads must be at least 10% of total ads
t > .1(t + r + n)
Constraint TV Radio Newspaper
Audience 100,000 18,000 40,000
Cost $2000 $300 $600
Max media usage 10 20 10
a) Max total audience
100,000t + 18,000r + 40,000n
$2000t + $300r + $600n < $18,200
t < 10
r < 20
n < 10
.1t - .1r - .1n < 0
-.5t + .5r - .5n < 0

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There should be 4 TV messages, 14 radio messages and 10 newspaper messages with a total
audience of 1,052,000 reached and a total budget of $18,200.
b)

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Audience reached would increase to 1,057,130, which is an increase of 5,130 audience members.
2. (10 points) Chapter 4 Problem 6.
Labor hours
Product Profit/unit Dept. A Dept. B
1 $25 6 12
2 $20 8 10
900 hours available labor
x1 = amount of product 1 to make
x2 = amount of product 2 to make
x3 = number of hours for Dep. A
x4 = number of hours for Dep. B
Max
25x1 + 20x2
x3 + x4 < 900
6x1 + 8x2 – x3 < 0
12x1 + 10x2 – x4 < 0

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3. (15 points) Chapter 4 Problem 8
x1 = number of officers at 8am
x2 = number of officers at noon
x3 = number of officers at 4pm
x4 = number of officers at 8pm
x5 = number of officers at 12am
x6 = number of officers at 4am

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Min
X1 + x2 + x3 + x4 +x5 + x6 < 38
X6 + X1 < 5
X1 + X2 < 6
X2 + X3 < 10
X3 + X4 < 7
X4 + X5 < 4
X5 + X6 < 6
3 officers 8am; 3 officers noon; 7 officers 4pm; 0 officers 8pm; 4 officers 12am; 2 officers 4am;
for a total of 19 officers

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4. (30 points) Chapter 4 Case Problem 1.
Budget < 279,000
Advertising media Exposure rating per
ad
Anew customers per
ad
Cost per ad
TV 90 4000 $10,000
Radio 25 2000 $3,000
Newspaper 10 1000 $1,000
TV
T1 = 90 exposure, 4000 customer < 10 ads
T2 = 55 exposure, 1500 customers > 10 ads
Radio
R1 = 25 exposure , 2000 customers < 15
R2 = 20 exposure, 1200 customers > 15
Newspaper
N1 = 10 exposure, 1000 customers < 20
N2 = 5 exposure, 800 customers > 20
Max exposure
90T1 + 55T2 + 25R1 + 20R2 + 10N1 + 5N1
Constraints
T1 < 10
R1 < 15
N1 < 20
4000T1 + 1500T2 + 2000R1 + 1200R2 + 1000N1 + 800N2 > 100,000
2R1 + 2R2 – T1 – T2 > 0
T1 + T2 < 20
10000T1 + 10000T2 > 140,000
3000R1 + 3000R2 < 99,000
1000N1 + 1000N2 > 30,000
10,000T1 + 10000T2+ 3000R1 + 3000R2+ 1000N1 + 1000N2 < 279,000