1. A retired couple supplement their income by making fruit pies, which they sale to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $5.50 to the grocer, and grape pies are sold for $5.20. The couple is able to sell all of the pies they produce. They use flour and sugar which purchase monthly. For the month of September, they have 1800 cup of sugar and 2100 cups of flour. Each apple pie requires 2 cups of sugar and 3 cups of flour, and each grape pie requires 3 cups of sugar and 3 cups of flour. The couple want to work no more than 60 hours making pies. Each apple pie takes 6 minutes, and each grape pie takes 3 minutes to make.
a. Determine the number of grape and apple pies that will maximize the revenues.
. Determine the amounts of sugar, flour, and time that will be unused.
2. Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%.
The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis's risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specifies that at least $300,000 be invested in the money market fund.
Let: S = number of units purchased in the stock fund
M = number of units purchased in the money market fund
Solve using the graphical procedure.
a. Determine how many units of each fund Innis should purchase for the client?
. How much annual income the investment will this investment strategy generates?
c. Suppose the client desires to maximize annual return. How should the fund be invested?
.
3. A project network is shown below. Use a forward and a backward pass to determine the critical path, and then fill out the table below.
Activity
Precedence Activities
Activity
Time (weeks)
ES
EF
LS
LF
Slack
Critical
Path?
A
--
5
B
--
4
C
--
8
D
A, B
4
E
C
12
F
C
10
G
D, E
3
H
E
2
I
E, F
5
a. Draw the project network.
. Complete a row for each activity under the column headings below.
c. Determine the Critical path QMB6