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Question 29851: If the demand d and the supply s for snowboards are d=360/p and s=150p-510 find the profit p, in hundreds of thousands of dollars, at the equilibrium point when supply and demand equal.
thanks for the help
Answer by ikdeep(226)   (Show Source):
You can put this solution on YOUR website! d=360/p ............(1)
s=150p-510 ..........(2)
it is given that at the equilibrium point when supply and demand equal.
thanks for the help,,so we get
360/p = 150p - 510
on multiplying both sides by p we get
360 = 150p^2 - 510p
or 0 = 150p^2 - 510p - 360
on dividing both sides by 30,, we get...
0 = 5p^2 - 17p - 360
Here you must know how we make factors i.e. splitting of the middle term...if you might not know then please contact me again and I will explain to you)... and we get......
0 = 5p^2 - (20 - 3)p - 360....solving the brackets wolud give...
0 = 5p^2 - 20p + 3p - 360
taking common from first two i.e. 5p^2 - 20p and last two i.e. 3p - 360
variables...we get
0 = 5p (p-4) + 3(p-4)..
or 0 = (5p + 3)(p - 4)..
You know that the product two numbers or variables becomes equal to zero if atleast one of them is zero....
therefore either (5p + 3) = 0
or (p - 4)= 0
if (5p + 3) = 0 the profit = -3/5
and since profit can't be in negative so this can't be values of profit
and if (p - 4)= 0 the profit = 4
or profit = 4 hundreds of thousands of dollars
hope this will help you
Please feel free to revert back for any further queries.
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