A manufacturer of nutritional products is formulating a new liquid vitamin supplement.
A bottle of the new product must contain at least 30 units of vitamin B and 50 units of
vitamin C. A unit of vegetable extract (V) contains 1.2 units of vitamin B and .8 units of
vitamin C. A unit of fruit extract (F) contains .25 units of vitamin B and 1.8 units of
vitamin C. The cost of vegetable extract is $.05 per unit and fruit extract costs $.06 per
unit. The firm’s goal is to minimize its cost per bottle. Formulate a linear programming
problem for the firm.
How does a bidder’s risk aversion affect on respective bidding strategies in the English
and sealed-bid auctions?
Suppose that a public project (for example, a golf course) is funded out of general tax
revenues. The proportion of the population benefiting from the project is split into a
high-income group and a low-income group, and 75% of the benefits go to the
high-income group. How does this information affect a benefit-cost analysis?
An item with a common unknown value is being sold via an English auction. Is there
any possibility of winner’s curse? Explain.
What are the conditions suitable for a seller to use an auction? Explain.
How does finite competition differ from infinite competition between rival firms?
Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The
firm’s cost function is: C = 200 + 4Q. In this case, how can the firm use marginal
revenue and marginal cost to maximize its profit?
If customer income increases over time, (while price is held constant), what is the most
likely impact on unit sales of a firm? Explain.
Amanda is a troubleshooter for a major manufacturing firm. A particular facility has
experienced problems with quality for several years. In addition, there have been some
major problems with the facility’s labor union. A bitter strike, lasting six months,
occurred prior to signing the current contract. Past management teams have visited and
inspected the site but have been unable to achieve change, despite detailed study and
recommendations. Recently, sales of the facility’s product line have declined in the face
of increased import competition from an East Asian country, and this is unlikely to
change in the near future. Currently, the Board is considering two new courses of
action. One is retooling the facility to manufacture a new line of products. This would
involve capital costs of several millions of dollars. It would also mean that there would
be no production from the facility while retooling and retraining takes place. The
second option is closing down the facility. This would involve costs in the form of
termination benefits, as well as funding some pension benefits of senior employees.
There appear to be no buyers for the plant, and it would likely remain idle for some
time, while continuing to be a tax drain on the company. How would Amanda use the
steps of decision-making and the concept of value maximization to recommend a
course of action to the Board? Explain.
Explain how Bayes Theorem is used to revise probabilities.