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1. A group of investors is considering developing a Resort Hotel complete with a championship level golf course on the picturesque banks of the Delaware Bay. The cost to purchase the land would be $1.2 million payable now. The construction costs however are uncertain. They are approximately $1.8 million payable at the end of the year. The costs could be higher or lower than $1.8 million by 20%. Describe this variability by a triangular distribution. The best estimate of the profit that would be generated in years 2, 3, 4 and 5 is $700,000. Because of the great uncertainty it’s considered that the profit in each of those years will vary about $700,000 according to a normal distribution with a standard deviation of $400,000. The profits each year are considered to be independent of the profits in other years and payable at the end of the year. After year 5 the investors plan to sell the hotel for an amount that varies uniformly between $6 and $10 million. The investors use a discount rate of 10% in the computation of NPV.

Use @Risk to perform 10000 trials of this investment scenario.

i) What is the mean NPV of the project?
ii) What is the estimated probability that the NPV will exceed $2 miilion?
iii) Compute the minimum of the operating profit over the four years and determine its mean over the 10,000 trials.
iv) Estimate the probability that the profit will be positive (>=0) over all four years.

2. Joe R. earns extra money as a wedding photographer. He delivers prints with dimensions 4×6, 5×7 or 8×10. He uses two types of photographic paper 8×10 and 8×12 and cuts them to accommodate the 4×6 and 5×7 prints. He has identified the patterns in the table below using the notation Xij where i=1 for patterns cut from an 8×10 sheet and i=2 for patterns cut from 8×12 sheets. 8×10 sheets cost $1 and 8×12 sheets cost $1.25.

Pattern 4×6 5×7 8×10
X10 0 0 1
X11 0 1 0
X12 0 2 0
X13 1 0 0
X14 2 0 0
X15 3 0 0
X16 1 1 0
X20 0 0 1
X21 0 1 0
X22 0 2 0
X23 1 0 0
X24 2 0 0
X25 3 0 0
X26 4 0 0
X27 1 1 0
X28 2 1 0
Joe has just received an order for the following numbers of prints

136 4×6 prints
41 5×7 prints
17 8×10 prints
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1) Assuming leftover portions of sheets have no value, find the number of sheets Joe must buy to meet this order. Compute the number of each size that are left over.
2) Compute the number of square inches of wasted material for each pattern. Reformulate and solve the problem to minimize the total amount of wasted material.

3. The Stackhouse Corporation has another product in which 3 components A, B and C are stacked on each other to form an assembly. A number of each component have been measured and classified as nominal or smaller or larger than nominal by 0.001in. The available number of each component of each size is tabled below. Construct a spreadsheet optimization model to determine how many assemblies of nominal height can be put together from these components. List the parts that are left over.
Part A B C
Dev(0.001) -1 0 +1 -1 0 +1 -1 0 +1
Available 4 10 8 5 12 8 9 11 5

4. A retirement community is spread out over several square miles. The area is divided into five tracts. It is desired to establish medical stations at two of the tracts. Each tract must be assigned to exactly one of the two stations. The table below gives the response time in minutes to a medical emergency in each tract as obtained for all possible locations of a medical station. Determine in which tracts the medical stations should be located and which tracts should be assigned to each station so as to minimize the average response time to a medical emergency.
Number of Tract Having a Medical Station

1 2 3 4 5
Tract 1 5 20 15 25 10
Tract 2 12 4 20 15 25
Tract 3 30 15 6 25 15
Tract 4 20 10 15 4 12
Tract 5 15 25 12 10 5
Use Solver Table to determine how the location of the stations and the average response time varies as the number of medical stations varies from 1 to 5.
5. A Department store sells 1200 cameras per year. The store orders its cameras from a regional warehouse and it takes a week for the cameras to arrive once an order is placed. The cost of placing an order is $125. The cameras cost $300 and are sold for $500. There is no physical storage cost but the store values cash at an annual interest rate of 8%. 1) Determine the optimum order quantity to minimize annual costs assuming no backlogging is allowed. 2) At what inventory level should an order be placed so that there is no backlog. 3) A service is available that can reduce the order cost to $50. What is the upper limit on how much the store should pay annually for that service? Show calculations.
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