Problem 1:
A steel mill produces two types of steel alloy: Boral and Chromal. Production of each alloy requires three processes: Box anneal, Cold Roll, and Strand anneal.
Production Capacities are:
Box anneal: 4,000 hours/month
Cold Roll: 500 hours/month
Strand anneal: 1,00 hours/month
Production rates in tons per hour are:
|
|
Box anneal
|
Cold roll pass 1
|
Strand anneal
|
Cold roll pass 2
|
|
Boral
|
4
|
72
|
11
|
36
|
|
Chromal
|
2
|
Not required
|
20
|
24
|
The maximum demand for Boral is 10,500 tons/month and for Chromal 6,000 tons/month. The contributions/ton are Boral: $25, and Chromal: $35.
What combination of Boral and Chromal maximizes total monthly contribution?
Problem 2:
The director of advertising for a retail chain is considering how to allocate her $200,000 budget for television advertising among four programs (A, B, C, D) on three channels (1, 2, 3). Market research studies have shown that the chain's customers can be broken down into two groups: "High-end Achievers" and "Aspiring Achievers" High-end Achievers spend twice as much in the store as do Aspiring Achievers. The director wants to maximize the total in-store spending potential of the audience but must have at least three ads on each program, and cannot spend more than 50% of the budget on any one channel. The audience by program and the ad cost are:
|
Channel
|
Program
|
Expected Audience
|
% High-End Achievers
|
% Aspiring Achievers
|
Cost/Ad
|
|
1
|
A
|
100,000
|
25
|
75
|
$7,500
|
|
1
|
B
|
50,000
|
60
|
40
|
$4,000
|
|
2
|
C
|
90,000
|
40
|
60
|
$6,500
|
|
3
|
D
|
80,000
|
50
|
50
|
$5,000
|
1. What is the most effective ad purchase ignoring the fact that the number of ads on any one program must be integer?
2. Include an integer constraint on the number of ads and re-solve.
3. Compare the two solutions.