26 May Question 3. (20 pts.) Solve the LP by Excel Solver and then answer the
Question
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
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