Find the equation of the plane passing through the intersection of the planes:
x + y +z + 1 = 0and 2x - 3y + 5z - 2 = 0 and the point (- 1, 2 , 1)
Mr. Nirav borrowed Rs. 50,000 from the bank for 5 years. The rate of interest is 9 % per annum compounded monthly. Find the payment he makes monthly if he pays back at the beginning of each month.
A dietician wishes to mix two kinds of food X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below:
Food | Vitamin A | Vitamin B | Vitamin C |
X | 1 unit | 2 units | 3 units |
Y | 2 units | 2 units | 1 unit |
One kg of food X costs Rs.24 and one kg of food Y costs Rs.36. Using Linear Programming, find the least cost of the total mixture which will contain the required vitamins.
A bill for Rs. 7650 was drawn on 8th March, 2013, at 7 months. It was discounted on 18th May, 2013 and the holder of bill received Rs. 7497. What is the rate of interest charged by bank?
The average cost function, AC for a commodity is given by AC = , in terms of output x. Find:
(i) The total cost, C and marginal cost, MC as a function of x.
(ii) The outputs for which AC increases.
(i) Let C be the total cost function. Then
Average cost (AC) =
Let MC be the marginal cost function. Then,
MC =
= 2x + 5
Now,
= 1 -
(ii) For AC to be increasing
Hence average cost increases if the output x is > 6.
Calculate the index number for the year 2014, with 2010 as the base year by the weighted aggregate method from the following data:
Commodity | Price in Rs. for 2010 | Price in Rs. for 2014 | Weight |
A | 2 | 4 | 8 |
B | 5 | 6 | 10 |
C | 4 | 5 | 14 |
D | 2 | 2 | 19 |
The quarterly profits of a small scale industry (in thousands of rupees) is as follows:
Year | Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
2012 | 39 | 47 | 20 | 56 |
2013 | 68 | 59 | 66 | 72 |
2014 | 88 | 60 | 60 | 67 |
Calculate four quarterly moving averages. Display these and the original figures graphically on the same graph sheet.