Cost-revenue-profit analysis

Ponderosa Development Corporation (PDC) is a small real estate developer that builds only one style

house.The selling price of the house is $115,000. Land for each house costs $55,000 and lumber,

supplies, and other materials run another $28,000 per house.Total labor costs are approximately $20,000 per house.

Ponderosa leases office space for $2,000 per month.The cost of supplies, utilities, and leased equipment runs another $3,000 per month.The one salesperson of PDC is paid a commission of $2,000 on the sale of each house.PDC has seven permanent office employees whose monthly salaries are given on the next slide.

a) Write the monthly cost function c (x), revenue function r (x), and profit function p (x).

b) What is the breakeven point for monthly sales of the houses?

c) What is the monthly profit if 12 houses per month are built and sold?

Time Series Analysis and Forecasting

Sales of Comfort brand headache medicine for the past 10 weeks at Rosco Drugs are shown below.If Rosco uses the nave forecast method to forecast sales for weeks 2 - 10, what are the resulting MAE, MSE, and MAPE values?

Linear Programming

Consider a chocolate manufacturing company which produces only two types of chocolate - A and B. Both the chocolates require Milk and Choco only.To manufacture each unit of A and B, following quantities are required:

Each unit of A requires 1 unit of Milk and 3 units of Choco

Each unit of B requires 1 unit of Milk and 2 units of Choco

The company kitchen has a total of 5 units of Milk and 12 units of Choco. On each sale, the company makes a profit of CAD 6 per unit A sold CAD 5 per unit B sold.

Now, the company wishes to maximize its profit. How many units of A and B should it produce respectively

Linear Programming: Sensitivity Analysis

Olympic Bike is introducing two new lightweight bicycle frames, the Deluxe and the Professional, to be made from special aluminum and steel alloys.The anticipated unit profits are $10 for the Deluxe and $15 for the Professional. The number of pounds of each alloy needed per frame is summarized bellow:

A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of the steel alloy weekly.

Aluminum Alloy Steel Alloy

Deluxe 2 3

Professional 4 2

a) How many Deluxe and Professional frames should Olympic produce each week?

b) Suppose the profit on deluxe frames is increased to $20.Is the above solution still optimal?What is the value of the objective function when this unit profit is increased to $20?

c) If the unit profit on deluxe frames were $6 instead of $10, would the optimal solution change?

Linear Programming: Integer

Eastborne Realty has $2 million available for the purchase of new rental property. After an initial screening, Eastborne reduced the investment alternatives to townhouses and apartment buildings. Each townhouse can be purchased for $282,000, and five are available. Each apartment building can be purchased for $400,000, and the developer will construct as many buildings as Eastborne wants to purchase.

Eastborne's property manager can devote up to 140 hours per month to these new properties; each townhouse is expected to require 4 hours per month, and each apartment building is expected to require 40 hours per month. The annual cash flow, after deducting mortgage payments and operating expenses, is estimated to be $10,000 per townhouse and $15,000 per apartment building. Eastborne's owner would like to determine the number of townhouses and the number of apartment buildings to purchase to maximize annual cash flow.

DECISION TREE ANALYSIS

Pittsburgh Development Corporation (PDC) purchased land that will be the site of a new luxury condominium complex. PDC commissioned preliminary architectural drawings for three different projects: one with 30, one with 60, and one with 90 condominiums.

The financial success of the project depends upon the size of the condominium complex and the chance event concerning the demand for the condominiums. The statement of the PDC decision problem is to select the size of the new complex that will lead to the largest profit given the uncertainty concerning the demand for the condominiums.

Consider the following problem with three decision alternatives and two states of nature with the following payoff table representing profits:

Thus, determine the better decision for this situation based on the three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable:

A) the optimistic approach

B) the conservative approach

C) the minimax regret approach

D) if the probability of the states of nature is known (s1 = 80% and s2 = 20%), is your decision being different?

BUSINESS DECISION ANALYSIS COURSE