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The Chemistry department at a local college decides to stock at least 900 small test tubes and 600 large test tubes. It wants to buy at least 2700 test tubes to take advantage of a special price. Since the small test tubes are broken twice as often as the large, the department will order at least twice as many small test tubes as large.
a) If the small test tubes cost 18 cents each and the large ones cost 15 cents each, how many of each size should be ordered to minimize cost?
b) Suppose the minimum number of test tubes is increased to 3000. Use shadow costs to calculate the total cost in this case.
Find the directional derivative at P(-2,2,-1) in the direction of Q(18,-2,4). Find the direction of maximum decrease at P. (your answer does not have to be unit vector.) What is the maximum rate of decrease?
To make a conjecture about the tangent lines and the graph with the proof of the conjecture - Find the distance between the functions is greatest, and prove your conjecture.
In 2001, 400 seat Boeing 747s were priced at $200 million each, 300 seat Boeing 777s were priced at $160 million, and 200 passenger Airbus A321s were priced at $60 million.
Probability that both circuits are defective, A factory worker places 93 newly created circuits on a shelf to be checked for quality. Of these, 8 will not work correctly. Suppose that she is asked to randomly select two circuits
By a line, a great circle on the sphere is referenced. Is it still true that two points determine a unique line? Is it still true that two distinct lines either meet in a single point or do not meet at all?
A pilot, attempting to fly from Middletown to Westburg, a distance of 200 miles, notices after flying 180 miles that West burg is still 35 miles away because the heading was off by a few degrees.
The volume of a rectangular prism is given by the formula V = lwh. What are the general dimensions of the prism if the volume is 6x3 +9x2 - 6x? You will not have an exact dimension but rather an expression that represents them.
An absent-minded nurse is to give Mr. Brown a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Brown will die is 1/3.
Write out the probability distribution for of sales during a five-day week. What is the mean and variance of this distribution? Assume that the profit from each sale is $750 for the situation in additional problem. What is the expected weekly profi..
The sum of three numbers is 6. The third number is the sum of the first and second numbers. The first number is one more than the thrid number. Find the numbers.
Cutter Enterprises purchased equipment for $72,000 on January 1, 2006. The equipment is expected to have a five-year life, with a residual value of $6,000 at the end of five years.
There are 10 workers and 2 administrators in a company meeting room. Two people will be selected at random without replacement. The chance that the second person is a worker is:
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