How much will you be willing to pay for additional amounts of fertilizer?
business
Description
Product Mix Problem
Your company
grows two types of plants, A and B (e.g., roses and begonias).
Both plant types
require two types of fertilizer throughout the growing season, Fertilizer 1 and
Fertilizer 2.
A single plant A
will require 2 pounds of fertilizer 1 and 1 pound of fertilizer 2.
A single plant B
will require 1 pound of fertilizer 1 and 2 pounds of fertilizer 2.
Your distributer
has 4000 pounds of fertilizer 1 and 5000 pounds of fertilizer 2 available for
delivery at the beginning of the season.
You know that
every plant A you grow will generate $2.25 profit, and every plant B you grow
will generate $2.60 profit.
1. How many of each plant should you grow if you
want to maximize profit for the season?
2. What amount of change in profit for plant A
and plant B will change your decision about product mix?
3. How much will you be willing to pay for
additional amounts of fertilizer?
4. If your fertilizer storage capacity is 8000
pounds, what is your new product mix, and how much of each fertilizer should
you order? What would you be willing to
pay for additional storage capacity?
Lockbox Problem
A major credit
card company (call it “MasterDebt”) receives checks from all different regions
in the country on a daily basis. Once
these checks are mailed, the time a check spends in the mail (called “float”)
creates loss for MasterDebt, for as soon as they receive the checks they can
cash them and collect interest on the funds.
MasterDebt can make 15% annual interest on their cash holdings (since
that’s what they charge their customers in credit card interest).
In order to
reduce the amount of float loss for these checks, MasterDebt is considering
opening “Lockbox” locations across the country where the checks can be received
and processed. The locations and the
projected annual cost of operations (labor and overhead) at each location are
as follows:
|
ANNUAL COSTS (X$1000) |
|||||
|
Sacramento |
Denver |
Chicago |
Dallas |
New York |
Atlanta |
|
25 |
60 |
35 |
35 |
30 |
35 |
The average
number of days that a check would float between each region and each lockbox
location is shown in the following chart.
|
AVERAGE FLOAT DAYS |
||||||
|
REGION |
Sacramento |
Denver |
Chicago |
Dallas |
New York |
Atlanta |
|
Central |
4 |
2 |
2 |
2 |
3 |
3 |
|
Mid-Atlantic |
6 |
4 |
3 |
4 |
2 |
2 |
|
Midwest |
3 |
2 |
3 |
2 |
5 |
4 |
|
Northeast |
6 |
4 |
2 |
5 |
2 |
3 |
|
Northwest |
2 |
3 |
5 |
4 |
6 |
7 |
|
Southeast |
7 |
4 |
3 |
2 |
4 |
2 |
|
Southwest |
2 |
3 |
6 |
2 |
7 |
6 |
The average daily
payments received from each region are shown in the following chart (in
thousands of dollars).
|
REGION |
Payments |
|
Central |
45 |
|
Mid-Atlantic |
65 |
|
Midwest |
50 |
|
Northeast |
90 |
|
Northwest |
70 |
