3. (20 pts.) Solve the LP by Excel Solver and then answer the following questions based on the Answer and Sensitivity Report of the original LP. You are not allowed to re-solve the LP for each of the questions.

(Note: please attach the Answer and Sensitivity Report of the following LP.)

Max where is the quantity of product 1 to make etc.

Subject to

Machine minutes

Labor hours

Materials pounds

Product 2 units

Non-negativity

a. Are any constraints binding? If so, which one(s)?

b. If the profit on product 3 were changed to $20 a unit, what would the values of the decision

variables be? The objective function? Explain.

c. If the profit on product 1 were changed to $20 a unit, what would the values of the decision

variables be? The objective function? Explain.

d. If the manager decided that as many as 18 units of product 2 could be produced (instead of 16),

how much additional profit would be generated?

e. If 5 minutes more of machine time were available, whether would the shadow price for the

machine constraint change? And how much would the value of the objective function changes?

 

2. A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson distributed. Determine:

(a) The average number of customer waiting in line

(b) The average time customers spend in the system

(c) The probability of waiting in queue longer than 1 minute

 

A small town with one hospital has two ambulances to supply ambulance service. Requests for ambulances during non-holiday weekends average 0.8 per hour and tend to be Poisson distributed. Travel and assistance time averages one hour per call and follows an exponential distribution. Find:

(a) System utilization

(b) The average number of customers waiting

(c) The average time customers wait for an ambulance

(d) The probability that both ambulances will be busy when a call comes in