SOLUTION: the profit P in dollars gained by selling x computers is modeled by the equation p(x)=5x2+1000x+5000. how many computers must be sold to obtain a profit of 55,000.00 what is the op

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Question 1151082: the profit P in dollars gained by selling x computers is modeled by the equation p(x)=5x2+1000x+5000. how many computers must be sold to obtain a profit of 55,000.00 what is the optimal number of computers to sell to earn the maximum profit
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


p%28x%29=5x%5E2%2B1000x%2B5000
to obtain a profit of p%28x%29=55000.00+, substitute given in formula above
55000.00=5x%5E2%2B1000x%2B5000......solve for x
55000.00-5000=5x%5E2%2B1000x
50000.00=5x%5E2%2B1000x
0=5x%5E2%2B1000x-50000...simplify
0=x%5E2%2B200x-10000...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-200+%2B-+sqrt%28+200%5E2-4%2A1%2A%28-10000%29+%29%29%2F%282%2A1%29+
x+=+%28-200+%2B-+sqrt%28+40000%2B40000+%29%29%2F2+
x+=+%28-200+%2B-+sqrt%28+2%2A40000+%29%29%2F2+
x+=+%28-200+%2B-+200sqrt%28+2+%29%29%2F2+...simplify
x+=+%28-100+%2B-+100sqrt%28+2+%29%29+

x+=100+%28-1%2B-+sqrt%28+2+%29%29+.........since x represents he optimal number of computers, disregard negative root
x+=100+%28-1%2B+sqrt%28+2+%29%29+
x+=100+%28-1%2B+1.4142135623730951%29+
x+=100+%280.42135623730951%29+
x+=41.42135623730951%29

the optimal number of computers to sell to earn the maximum profit is 41 rounded to whole number
check:
p%28x%29=5%2A41%5E2%2B1000%2A41%2B5000
p%28x%29=5%2A1681%2B41000%2B5000
p%28x%29=8405%2B41000%2B5000
p%28x%29=54405->less because rounding (we cannot sell fraction 0.42135623730951 of it)
what is the optimal number of computers to sell to earn the maximum profit?
your function p%28x%29=5x%5E2%2B1000x%2B5000 does not have a maximum (no global maxima found)


Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.

In part,  related to a "maximum profit",  the formulation of your problem is   W R O N G.

I think that the error is in the formula for the polynomial p(x).


Twice and thrice check it (!)