Math Answers

A firm produces two commodities, ×, and y. The demand functions are

P, = 900 - 2x - 2 y

and

P, = 1400 - 2x -4y

respectively, where P, is the price of commodity x and P, is the price of commodity y. The costs

are given by

C, = 7000 + 100x + x2

and

C, = 10000 + 6 y*

a) Show that the firm's profit function is given by

7 (x, y) = -3x? - 10y? 4xy + 800x +1400y -17000

b) Suppose the firm is required to produce a total of exactly 60 units. Find the values of x

and y that maximize profits.

In a study made on time and motion, it was found out that a certain manual work can be finished at an average time of 40 minutes with a standard deviation of 18 minutes. A group of 16 workers is given a special training and then found to average only 35 minutes. Can we conclude that the special training can speed up the work using a 0.05 level? 

2. A random sample of 40 boys showed a mean weight of 120 lbs. with a standard deviation

of 12lbs. The standard weight for their age category is about 130lbs. Test the hypotheis that the selected boys are significantly lighter than the standard weight at0.01 level of siginificance.

Construct the sampling distribution of the sample mean for the population that consists of the scores 15, 18, 11, 14, 17, with a sample size of 3. Compute as well the mean of the sampling distribution using the expected value of the distribution and verify the result by computing for the population mean.

it is claimed that the average monthly income of chemical engineers last year was P27,900.00 A random sample of 36 chemical engineers is selected and it is found out that the average monthly salary is P28,000.00 Using a 0.05 level of significance can it be concluded that there is an increase in the average monthly income of chemical engineers? Assume that the population standard deviation is P250.50

If the distribution is not normally distributed and the sample size is small ,n=10, is the t-test still apropriate to use?explain your answer

Use Green’s Theorem to evaluate

∮C(x − 2y2) dx + (y4 + 2xy) dy where C consists of the line segment

from (0, 2) to (0, 4), followed by the curve with parametric equations x = 4 cos t, y = 4 sin t from (0, 4) to (−2, 2√3), then the line segment from (−2, 2√3) to (−1, √3), and finally the curve with parametric equations x = 2 sin t, y = 2 cos t from (−1, √3) to (0, 2).

Find the mean, variance and standard deviation of the following measures 2,5,6,3,9,10,12

2. The population mean length of a chocolate wafer stick is 86 mm long with a standard deviation of 6 mm. A sample of 20 sticks are taken. What is the probability that

a. the sample mean is not less than 84 mm?

b. the sample mean is not more than 87 mm?

c. the sample mean differs from the population mean by at most 4 mm?

The manufacturer of a new drug claims that it will lower

blood pressure by 13 points on the average. When the drug was

administered to 6 patients, the following drops in blood pressure

were registered: 12, 8, 15, 9, 10 and 16. Is the claim sustained at

the 0.05 level of significance.