Question

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:

Type of Loan/Investment	Annual Rate of Return (%)
Automobile loans	8
Furniture loans	10
Other secured loans	11
Signature loans	12
Risk-free securities	9

The credit union will have $2 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:

• Risk-free securities may not exceed 30% of the total funds available for investment.

• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).

• Furniture loans plus other secured loans may not exceed the automobile loans.

• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2 million be allocated to each of the loan/investment alternatives to maximize total annual return?

Type of Loan/Investment	Fund Allocation
Automobile loans	$
Furniture loans	$
Other secured loans	$
Signature loans	$
Risk-free securities	$

What is the projected total annual return?

Annual Return = $

The Clark County Sheriff’s Department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty:

	Time of Day	Minimum No. of Officers on Duty
	8:00 a.m.–noon	5
	Noon–4:00 p.m.	6
	4:00 p.m.–8:00 p.m.	8
	8:00 p.m.–midnight	7
	Midnight–4:00 a.m.	4
	4:00 a.m.–8:00 a.m.	6

Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times to minimize the total number of officers required. (Hint: Let x₁ = the number of officers beginning work at 8:00 a.m., x₂ = the number of officers beginning work at noon, and so on.) If your answer is zero, enter “0”.

	Starting Time	Officers Starting
	8:00 a.m.
	Noon
	4:00 p.m.
	8:00 p.m.
	Midnight
	4:00 a.m.

Answer 1