Answers by visitors named: Clem
Given cost function
C= 0.025x^2 +13x+100
Each unit is sold for ksh 20.
Hence revenue function , R= 20x
Where, X is the no. Of products
A) to ensure there is no loss, the cost function should be equal to revenue function.
That is 0.025x^2+ 13x + 100 = 20x
0.025x^2 + 13x -20x +100 =0
0.025x^2 - 7x +100= 0
Dividing the equation by 0.025
x^2 -(7/0.025) x + 100 /0.025 = 0
x^2 - 280x + 4000 = 0
By solving using the formula
x = (-b +- √(b^2 - 4ac))/2a
Where a= , b= -280 , c= 4000
we get x= 265 , 15
To ensure no loss 265 is selected.
Hence minimum 265 unit should be produced to ensure there is no loss occur.
B) selling price is incresed by 45%
Hence new selling price = 20+ 20*45/100
= 20+ 9 = 29
Hence revenue function = 29x
To ensure no loss = . 025x^2 + 13x + 100 = 29x
Tht is 0.025x^2 +13x +100-29x =0
0.025x^2 -16x + 1000=0
By dividing throughout by 0.025
x^2 - 640x + 4000= 0 by solving
With a=1 , b= -640 and c= 4000
We get x = 634 , 6.
To ensure no loss 634 is selected.
Hence to ensure no loss production level should be 634 products