A person borrows 68,962 on the condition that he will repay the money with compound interest at 5 % per annum, installments, the first one being payable at the end of the first year. Find the value of each installment.
A company manufacturers two types of toys A and B. a toy of type a requires 5 minutes for cutting and 10 minutes for assembling. A toy of type B requires 8 minutes for cutting and 8 minutes for assembling. There are 3 hours available for cutting and 4 hours available for assembling the toys in a day. The profit is 50 each on a toy of type A and 60 each on a toy of type B.. How many toys of each type should the company manufacture in a day to maximize the profit? Use linear programming to find the solution.
The piece of six different commodities for years 2009 and year 2011 are as follows:
Commodities | A | B | C | D | E | F |
Price in 2009() | 35 | 80 | 25 | 30 | 80 | x |
Price in 2011() | 50 | y | 45 | 70 | 120 | 105 |
The index number for the year 2011 taking 2009 a sthe base year for the aove data was calculated to be 125.. Find the values of x and y if the total price in 2009 is 360.
The number of road accidents in the city due to rash driving, over a period of 3 years, is given in the following table:
Year | Jan - Mar | April - June | July - Sept. | Oct. - DEc. |
2010 | 70 | 60 | 45 | 72 |
2011 | 79 | 56 | 46 | 84 |
2012 | 90 | 64 | 45 | 82 |
Calculate four quarterly moving averages and illustrate them and original figures on one graph using the same axes for both.
Year | Quarter | Values | 4-quarterly moving total | 4-quarterly moving average | 4-quarterly moving average centered |
2010 | I | 70 | |||
II | 60 | ||||
247 | 24/4 = 61.75 | ||||
III | 45 | 125.75/2 = 62.875 | |||
256 | 256/4 = 64.00 | ||||
IV | 72 | 127/2 = 63.500 | |||
252 | 252/4 = 63.00 | ||||
2011 | I | 79 | 126.25/2 = 63.125 | ||
253 | 253/4 = 63.25 | ||||
II | 56 | 129.25/2 = 64.750 | |||
265 | 265/4 = 66.25 | ||||
III | 46 | 135.25/2 = 67.625 | |||
276 | 276/4 = 69.00 | ||||
IV | 84 | 140/2 = 70.000 | |||
284 | 284/4 = 71.00 | ||||
2012 | I | 90 | 141.75/2 = 70.875 | ||
283 | 286/4 = 70.75 | ||||
II | 64 | 141/2 = 70.500 | |||
281 | 281/4 = 70.25 | ||||
III | 45 | ||||
IV | 82 | ||||
A firm has the cost function C = and demand function x = 100 - p
(i) Write the total revenue function in terms of x.
(ii) Formulate the total profit function P in terms of x.
(iii) Find the profit maximising level of output x.
A bill of Rs. 5050 is drawn on 13th April 2013. It was discounted on 4th July 2013 at 5 % per annum. If the banker's gain on the transaction is Rs. 0.50, find the nominal date of the maturity of the bill.