Problem 1: Suppose you are on a weekend trip to a city that is d miles away. Develop a model that determines your round trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you?
Problem 2: For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand. Let
D= annual demand for a product in units
P= price per unit
Assume that a firm accepts the following price demand relationship as being realistic:
D= 800-10p
Where p must be between $20 and $70
A. How many units can the firm sell at the $20 per unit price? At the $70 per unit price?
B. Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price.
C. Based on other considerations, the firm's management will only consider price alternatives of $30 $40 and $50. Use your model from part (b) to determine the price alternative that will maximize the total revenue.
D. What are the expected annual demand and the total revenue according to your recommended price?
Problem 3: Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $300 per student. The cost for the conference room, instructor compensatipn , lab assistants, and promotion is $4800. Micromedia rents computer for its seminars at a cost of $30 per computer per day.
A. Develop a model for the total cost to put on the seminar. Let x represent the number of students who enroll in the seminar.
B. Develop a model for the total profit if x students enroll in the seminar.
C. Micromedia has forecasted an enrollment of 30 students for the seminar. How much profit will be earned if their forecast is accurate?
D. What is the breakeven point?
Problem 4: Preliminary plans are underway for the construction of a new stadium for a major league baseball team. City officials question the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individual may buy the boxes for $100,000 each. The fixed construction cost of $50,000 for each box constructed.
A. What is the breakeven point for the number of luxury boxes in the new stadium?
B. Preliminary drawings for the stadium show that the space is available for the construction of up to 50 luxury boxes. Promoters indicate that buyers are available and that all 50 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes? What profit is anticipated?
Problem 5: Let A be an event that a person's primary method of transportation to and from work is an automobile and B be an event that a persons primary method of transportation to and from work is a bus. Suppose that a large city P(A) =0.45 And P(B)= 0.35
A. Are events A and B mutually exclusive ? What is the probability that a person uses an automobile or a bus in going to and from work?
B. Find the probability that a person's primary method of transportation is some means other than a bus.