ECON 134A Midterm: ECON 134A UCSB Test3A solution sketches 2012Spring

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turquoisegnu128

31 Jan 2019

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Find all values of the constant c that make the function f (x) continuous on ( , ). f (x) = ( c2x2 3x 1, Therefore c = 4, 1. f (x) = f (1). Find the linear approximation of the function f (x) = sin (2x) at a = answer: f ( . Find the derivative of the function f (x) = 3x 1 using the limit de - nition of the derivative. No credit will be given if limit de nition is not used. answer: f (x) = lim h 0 q3(x + h) 1 3x 1 h. = lim h 0 q3(x + h) 1 3x 1 (3(x + h) 1) (3x 1) h(q3(x + h) 1 + 3x 1 h. Q3(x + h) 1 + 3x 1 q3(x + h) 1 + 3x 1. Find an equation of the tangent line to the curve. 4q3x y = x y + 9.

Related Questions

Need assistance with these problems!

1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X₁ + X₂ + X₃ + X₄
Subject to: X₁ + X₄%u2265 12 (shift 1)
X₁ + X₂%u2265 15 (shift 2)
X₂ + X₃%u2265 16 (shift 3)
X₃ + X₄%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above

2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)

finding the profit at every corner point of the feasible region to see which one gives the highest value.
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
locating the point that is highest on the graph.
none of the above.
all of the above.

3. Multiple optimal solutions can occur when the objective function is __________ a constraint line. (Points : 3)

unequal to
equal to
linear to
parallel to

4. When applying linear programming to diet problems, the objective function is usually designed to: (Points : 3)

maximize profits from blends of nutrients.
maximize ingredient blends.
minimize production losses.
maximize the number of products to be produced.
minimize the costs of nutrient blends.

5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 3)

same product mix, different total profit.
different product mix, same total profit as before.
same product mix, same total profit.
different product mix, different total profit.

6. The corner point solution method: (Points : 3)

will yield different results from the isoprofit line solution method.
requires that the profit from all corners of the feasible region be compared.
will provide one, and only one, optimum.
requires that all corners created by all constraints be compared.
will not provide a solution at an intersection or corner where a non-negativity constraint is involved.

7. Consider the following linear programming problem.
Maximize 4X + 10Y
Subject to: 3X + 4Y %u2264 480 and 4X + 2Y %u2264 3 360
all variables %u2265 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).

What is the maximum possible value for the objective function? (Points : 3)

1032
1200
360
none of the above

8. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is: (Points : 3)

guessing the values of the variables.
putting in a value for the objective function.
choosing the options for assuming both a linear model and non-negative variables.
resetting the parameters.
none of the above.

9. Consider the following linear programming problem.
Maximize 5X + 6Y
Subject to: 4X + 2Y %u2264 420 and 1X + 2Y %u2264 120
all variables %u2265 0

Which of the following points (X,Y) is not feasible? (Points : 3)

(50,40)
(20,50)
(60,30)
none of the above

10. ____________ is used to analyze changes in model parameters. (Points : 3)

Optimal solution
Feasible solution
Sensitivity analysis
None of the above

Refer to the example of the Cobb-Douglas production function discussed in class, where the GDP (Y), Total Employment (X2 ), and Stock of Fixed Capital (X3 ), are measured for the output, labor input and capital input, respectively. The following model is fitted and the R output is below. The data are yearly data from 1955 to 1974.

lnY = B1 +B2lnX2 + B3lnX3 + u

a. Interpret the coefficient estimate of B3 specific to this problem.

b. Find the rate of change of Y with respect to the change of X2 , at Y=218506.3 and X2=11152.6, and X3 = 340072.45.

c. Find the estimate of the return to scale parameter. (3 pts.)

d. Is there strong evidence that the GDP is inelastic relative to the stocks of fixed capital? Justify your answer at a=0.05.

e. Test if there is a positive (first order) autocorrelation in the error term using a=0.05 . Make sure to state the null and alternative hypotheses, to provide the values of the test statistic and the critical value(s), and to draw a conclusion. (6 pts.)

Regression output for Problem 3.

> fit<-lm(log(y) ~ log(x2) + log(x3))

> summary(fit)

Call:

lm(formula = log(y) ~ log(x2) + log(x3))

Residuals:

Min 1Q Median 3Q Max

-0.057142 -0.016250 -0.005793 0.023512 0.038739

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -1.65233 0.60619 -2.726 0.0144 *

log(x2) 0.33972 0.18569 1.830 0.0849 .

log(x3) 0.84600 0.09335 9.063 6.42e-08 ***

Signif. codes: 0 0.001 0.01 0.05 0.1 1

Residual standard error: 0.02829 on 17 degrees of freedom

Multiple R-squared: 0.9951, Adjusted R-squared: 0.9945

F-statistic: 1719 on 2 and 17 DF, p-value: < 2.2e-16

Durbin-Watson Statistic = 0.425618

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ECON 134A Midterm: ECON 134A UCSB Test3A solution sketches 2012Spring

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