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.
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.
(i) Total revenue function = x(100 - x)
Profit function = Revenue function - Cost function
= 100x - x2 - (x3/3 - 7x2 + 111x + 50)
= - x3/3 + 6x2 - 11x - 50
dP/dx = - x2 + 12x - 11
For maximum or minimum dP/dx = 0
x2 + 12x + 11 = 0
x = 1, 11
d2P/dx2 = - 2x + 12
= - 2 11 + 12
= - 10 < 0
Profit is maximum when x = 11
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.