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A clever but ethically corrupted mathematics student used to sell assignment solutions to her lazy fellow students. The student, however, learned that she can make much more money by charging the students fees for doing the assignments with them. This semester the students need to complete three assignments. One in Statistical Models, one in Introduction to Partial Differential Equations and one very difficult one in Optimization and Financial Mathematics. It takes 2 hours to explain the assignment to one student for Statistical Models, 1/2 hours for Introduction to Partial Differential Equations and 5 hours for Optimization and Financial Mathematics. The student can charge 5$, 50 Cents and 10$ per hour for Statistical Models, Introduction to Partial Differential Equations and Optimization and Financial Mathematics, respectively. In Statistical Models there are not more than 10 students wanting her service. In Introduction to Partial Differential Equations there are more than 50 students wanting her service and she has obligations to take at least 50. In Optimization and Financial Mathematics, the course with the most diligent students, there are not more than 2 students wanting her service. How many students from each course will the clever student offer her service to maximize her profit, if she does not want to spend more than 50 hours on the assignments?
(a) Formulate this as a linear programming problem
(b) Solve the problem using the two-phase simplex algorithm.
Subtract row 2 from row 1, row 3 from row 2, and so on, and explain why this does not change the determinant of the matrix.
Let the random variable X be the number of healthy parrots in the sample. Find the probability distribution of X.
How fast is the distance between the automobile and the farmhouse increasing when the automobile is 1.4 km past the intersection of the highway and the road?
If a ball is thrown straight up into the air with an initial velocity of 45 ft/s, it height in feet after t second is given by y=45t-16t2. Find the average velocity for the time period begining when t=2 and lasting.
Solve the given equation
the height of a ball thrown by a child is given by:-1/12x2+2x+4where x is the horizontal distance from the point at which the ball is thrown. What is the maximum height of the ball?
find the height of the flag pole from the word problem.the total height of a building and the flagpole on the roof is
How much nitrogen fertilizer per acre should the farmer use to maximize his net dollar return per acre? If the farmer uses the optimum amount of fertilizer what will be his net dollar return per acre?
A person hired a firm to build a CB radio tower.The firm charges $100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the next 10 feet will cost $125, ..
Jerry has a total of 23 marbles. The marbles are either blue or green. He has three more blue marbles than green marbles. How many green marbles does he have?
The perimeter of a rectangular playing field is 244 feet. If its length is 2 feet longer than twice its width, what are the dimensions of the field?
Find the Taylor's formula for estimation of cosine function
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