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1. (Curve Fitting:) A quantity y is known to depend upon another quantity x. A set of corresponding values has been collected for x and y and is presented in the Table below
X
0.0
0.5
1.0
1.9
2.5
3.0
3.5
Y
0.9
0.7
2.0
2.4
3.2
a) Fit the best straight line y = bx + a to this set of data points. The objective is to minimize the sum of absolute deviation of each observed value of y from the value predicted by the linear relationship. Write this as a linear programming model
b) Fit the best quadratic line y =cx2 + bx + a to this set of data points. The objective is to minimize the sum of absolute deviation of each observed value of y from the value predicted by the linear relationship. Write this as a linear programming model
Find the complete (including values for slack variables) optimal solution to this linear programming problem using. graphical method
The slopes in the direction field are all identical along horizontal lines and new solutions can be generated from old ones by time shifting (i.e., replacing y(t) with y(t - t0).
1. The term paper should examine an empirical research question in Economics. 2.The term paper should consist of a full documentation of the project in the form of Word and script file containing the computation codes.
Formulate a linear programming model for this problem. Solve the model with Excel Solver. Interpret your solution. If you have the chance to buy additional land at the price of $50 per acre, would you prefer to do so? What if the price would be $70..
Assuming these percentages remain valid over a long period of time, how many customers can the company expect to have in each category in the long run?
An irrigation scheme is fed from a river via a diversion channel. The irrigation channel is 2 m wide and is constructed of concrete with an estimated value of 0.019 for the Manning n. The bed slope is 0.0025.
Company BDC is implementing a new employee bonus system. While normal pay raises for personnel will be granted as in the past, the new system will choose the top employees for an additional $1,000 bonus.
1. Use the field axioms and their consequences to prove the following properties of real numbers. Your proofs should be careful and complete, with only one axiom, theorem, or other justification per step.
Explain what each of the following mathematical statements mean in regard to the graph of f(x).With your explanation, include a DIAGRAM for each part.
Question 3: The null hypothesis for the test of independence states that no correlation exists between the variables.
a. Derive the concentration profile of pyruvate in the film.
Determine the Cartesian equation of the plane that has x-, y-, and z-intercepts at 2, -4, and 3 respectively and determine the Cartesian equation of the plane that passes through the origin and is parallel to the plane in part a.
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