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d. How does the solution change if an additional 15 units of RHS are added
for each of the nutrition constraints? Add them one at a time; for example,
change 200 to 215, then 180 to 195, etc.
9. You have joined a CD club and you are required to purchase two types of
music CD’s in a year: Country Music (X) and Easy Listening (Y). Your con-
tract requires you to purchase a minimum of 20 Country CDs. Your contract
also requires you to purchase at least 20 Easy Listening CDs. Additionally, you
must purchase a minimum of 50 CDs (both types—Country Music and Easy
Listening) yearly. If the Country CDs cost \$7 per CD and the Easy listening
cost \$10 per CD, what is the solution that minimizes your yearly investment in
CDs?
a. Solve this LP with Solver.
b. Which constraints are binding?
c. Will the optimal solution (number of each CD type) change if the cost of
Country CD’s increases to \$9?
10. You are interested in obtaining a mortgage to ﬁnance a home. You borrow a
principal of \$150,000 for 30 years. If you would like to have a monthly payment
of \$700, what is the interest rate that will permit this payment?
11. The CUMPRINC() function is similar to the CUMIPMT() function, except
rather than calculate the cumulative interest paid, the function calculates the
cumulative principal paid in a period of time. You have a mortgage loan at 6%
over 30 years for \$150,000.
a. Use Goal Seek to ﬁnd the approximate period in which \$5,000 in principal
payments have been accumulated.
b. Use Goal Seek to ﬁnd the approximate period in which \$75,000 in principal
payments have been accumulated.
c.
If the use of Goal Seek is problematic for problem 11b, what do you sug-
gest as an alternative to ﬁnding the approximate period that still uses the
CUMPRINC() function?
12. Advanced Problem— Shift Scheduling Problem - I run a call center for cus-
tomers using my personal sensitivity training tapes. I guarantee that an
understanding and caring voice (UCV) will be available to customers 24 hours
a day. In order to satisfy this promise I must schedule UCV s based on histori-
cal demand data shown in the table below. I must determine how many UCV s
must report to work at the beginning of each Period. Once a worker reports for
duty they will work an 8-hour shift. There is no restriction in which of the peri-
ods a worker starts a shift. For example, if a worker begins at 3 pm, then they
will work until 11 pm.
a. Formulate and solve the LP that will minimize the total workers needed
to cover the overall UCV historical demand. Note that the assignment of a
partial worker is not a realistic situation. Therefore you may have to consider
a constraint that guarantees integer UCV’s.
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