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A company has to decide whether to invest in a large and expensive new plant or in a small and cheaper new plant or in no plant at all. With the big and expensive plant and a favorable market, they estimated a $350,000 net present revenue over the next 5 years. If the market will not be favorable, they estimated a $100,000 net present total revenue. With the small plant, they estimated a $250,000 and $80,000 net present total revenue, respectively. The two plants costs $200,000 and $150,000, respectively. If the company estimates that the market will be favorable with 60% probability and unfavorable with 40% probability, (iv) advise them on which plant to invest on.
The company could also commission a $20,000 survey that can predict with more precision the future of the market. If the survey predicts a favorable market (you may still use the 60% probability for this), the market will be be favorable with a 80% probability, and if the survey predicts an unfavorable market (you may still use the 40% probability for this), the market will be be favorable with a 90% probability 1. In other words, the company would be paying a few dollars for a survey to give them more confidence before they decide whether or not to commit to a big dollar investment. Should the survey be commissioned?
Prove Theorem 1.5.1. Theorem 1.5.1. The following assertions are equivalent for a graph T: Show that every tree T has at least ?(T) leaves.Show that a tree without a vertex of degree 2 has more leaves than other vertices. Can you find a very short pr..
Find an estimator of the parameter using the method of moments - find a sufficient statistic for the parameter and find sufficient statistics for the parameters.
determine if the solution is unique.
TO stop a base runner standing on first base from stealing second base, the catcher must throw the ball directly from home plate to second base. Which best represents this distance?
Membership in a Civic Organization In a civic organization, there are 38 members; 15 are men and 23 are women. If 3 members are selected to plan the July 4th parade, nd the probability that all 3 are women. Would you consider this event likely or ..
A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=-2A. Fine the vales of a and b
Primal LP and Optimal, Find the dual to this primal LP and its optimal solution
A certain bacteria population is known to quadruples every 30 minutes. Suppose that there are initially 80 bacteria.
What sample size will you use? You may assume that this sample size is used for the remainder of the problem.
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
The annual sales of romance novels follows a normal distribution, however the mean and std deviation are not known. 40% of the time the sales exceed 470,000 books and 10% of the time sales exceed 500,000 books. What is the number of books sold in ..
What is the probability that the business man's third flight is on time for at least two of his trips during the year?
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