Download EMBA 512 Modeling Examples Fall, 2015

EMBA 512
Modeling Examples
Fall, 2015
Copy Shop Breakeven Analysis

You are considering opening a small copy shop. It costs $5,000 to rent a copier for a year. It
costs $0.03 per copy to operate the copier. Other fixed costs of running the shop come to
$400 per month. The average charge per copy is $0.10. The shop will be open 365 days per
year. Each copier rented can make up to 100,000 copies per year.
a. For 1-5 copiers rented and daily demands of 500, 1000, 1500, and 2000 copies per day,
compute the annual profit for each combination of copiers rented and daily demand.
b. If 3 copiers are rented, what daily demand for copies is required to breakeven?
Product Mix Determination

The Monet Company produces four types of picture frames. The four frames are
different in terms of their size, shape, and materials. The table below shows the skilled
labor, metal, and glass used in constructing each frame type. The table also shows the
selling price for each frame. The unit costs are $8.00 per labor hour, $0.50 per ounce of
metal, and $0.75 per ounce of glass. During the coming week Monet has 4,000 hours of
skilled labor, 6,000 ounces of metal, and 10,000 of glass available. Market demand is
such that no more than 1,000 frames of type 1, 2,000 frames of type 2, 500 type 3 frames,
and 1,000 frames of type 4 can be sold. How many frames of each type should Monet
produce next week to maximize profit?
Frame
Skilled Labor
Metal
Glass
Selling Price
Frame 1
2
4
6
$28.50
Frame 2
1
2
2
$12.50
Frame 3
3
1
1
$29.25
Frame 4
2
2
2
$21.50
Pricing & Demand Estimation

A company produces and sells a product. The company wants to determine the price
that maximizes its profit from this product. The unit cost of producing and marketing
the product is $50. The company will charge at least $50 for the product to ensure
that it makes some profit. However, the market for the product is competitive and
demand falls sharply when prices are increased. Assume the company has estimated
two points on the demand curve for this product. Specifically, suppose the company
estimates that demand will be 400 units when price is $70 and 300 units when price is
$80. How should the company proceed in determining a price that will maximize
profits for this product?
Plant Capacity Analysis

Assume the demand for the drug Wozac during the current year is 50,000, and demand will
grow at 5% per year. If we build a plant that can produce x units of Wozac per year, it will
cost us $16x. Each unit of Wozac is sold for $3. Each unit of Wozac produced incurs a
variable production cost of $0.20. It costs $0.40 per year to operate a unit of capacity.
Determine how large a Wozac plant to build to maximize expected profit over the next ten
years. (Hint: forget about plant depreciation. To facilitate the analysis just keep track of
demand, capacity, production, revenue, fixed cost, variable cost, operating cost, and profit.
Use a data table to help determine the sensitivity of profit to changes in capacity. The
capacity with the highest profit will be the “best” decision).
Dynamic Pricing

A department store has purchased 5,000 swimsuits to be sold during the summer sales season.
The season lasts three months and the store manager forecasts that customers buying early in
the season are likely to be less price sensitive and those buying later in the season are likely
to be more price sensitive. The demand curves in each of the three months are forecast to be
as follows: d1 = 2,000 – 10p1, d2 = 2,000 – 20p2, and d3 = 2,000 – 30p3. If the department
store is to charge a fixed price over the entire season, what should it be? What is the resulting
revenue? If the department store wants dynamic prices that vary by month, what should they
be? How does this affect profits relative to charging fixed prices? If each swimsuit costs $40
and the store plans to charge dynamic prices, how many swimsuits should it purchase at the
beginning of the season?
Widgetco Simulation

It is equally likely that annual unit sales for Widgetco’s widgets will be low or high. If sales
are low (60,000), the company can sell the product for $10 per unit. If the sales are high
(100,000), a competitor will enter the market and Widgetco can sell the product for only $8
per unit. The variable cost per unit has a 25% chance of being $6, a 50% chance of being
$7.50, and a 25% chance of being $9. Annual fixed costs are $30,000
a. Suppose that unit sales, variable cost and unit price are equal to their respective expected
values—so that there is no uncertainty. Determine Widgetco’s annual profit for this scenario.
b. Use simulation, performing 400 replications, to estimate Widgetco’s expected annual profit.
c. Construct a 95% confidence interval for Widgetco’s annual expected profit.
Capacity Simulation Analysis

NuFeel is going to manufacture the drug Wozac. Demand during each of the next ten years
for Wozac is thought to be normally distributed with a mean of 50,000 and a standard
deviation of 12,000. NuFeel needs to determine how large a plant to build to maximize its
expected profit over the next 10 years from selling Wozac. If the company builds a plant that
can produce x units of Wozac per year, it will cost $16 for each of those x units (this cost is
incurred in the first year only). NuFeel cannot hold Wozac in inventory from one year to the
next, so each year’s production will be the smaller of the expected demand in that year or the
plant capacity. Each unit of Wozac sells for $3.70. Each unit of Wozac produced incurs a
variable production cost of $0.20. It costs $0.40 per year to operate a unit of capacity.
a. Among the capacity levels of 40,000, 45,000, 50,000, 55,000, 60,000, 65,000, and 70,000
units per year, which level maximizes expected profit? Use simulation to answer this
question. Do not worry about depreciation in this exercise. Replicate the simulation for
each capacity alternative 25 times.
b. For each capacity level under evaluation, compute the maximum 10-year profit, the
minimum 10-year profit, the average 10-year profit, the standard deviation of 10-year
profit, and the 95% confidence interval for the expected 10-year profit, based on the 25
replications. What capacity level do you recommend?