SOLUTION: The total cost(in dollars) for a company to manufacture and sell x items per week is C=60x+300, where as the revenue brought in selling all x items is R=100x-0.5x^2 . How many item

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The total cost(in dollars) for a company to manufacture and sell x items per week is C=60x+300, where as the revenue brought in selling all x items is R=100x-0.5x^2 . How many item      Log On


   



Question 452984: The total cost(in dollars) for a company to manufacture and sell x items per week is C=60x+300, where as the revenue brought in selling all x items is R=100x-0.5x^2 . How many items must be sold to obtain a weekly profit of $300?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Profit is (revenue - cost)
R+=+100x+-+.5x%5E2%0D%0A%7B%7B%7BC+=+60x+%2B+300+
+R+-+C+=+100x+-+.5x%5E2+-+60x+-+300+
+P+=+-+.5x%5E2+%2B+40x+-+300+
+300+=+-+.5x%5E2+%2B+40x+-+300+
+-+.5x%5E2+%2B+40x+-+600+=+0+
+-+5x%5E2+%2B+400x+-+6000+=+0+
+-+x%5E2+%2B+80x+-+1200+=+0+
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-1+
+b+=+80+
+c+=+-1200+
x+=+%28-80+%2B-+sqrt%28+80%5E2+-+4%2A%28-1%29%2A%28-1200%29+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-80+%2B-+sqrt%28+6400+-+4800+%29%29%2F%28%28-2%29%29+
x+=+%28-80+%2B-+sqrt%28+1600+%29%29%2F%28%28-2%29%29+
x+=+%28-80+%2B+40%29%2F%28%28-2%29%29+
+x+=+20+
and, using the negative root
x+=+%28-80+-+40%29%2F%28%28-2%29%29+
+x+=+60+
Selling either 20 or 60 items per week will
give a profit of $300
Here's a graph of solutions and the profit curve:
+graph%28+400%2C+400%2C+-50%2C+70%2C+-50%2C+500%2C+-x%5E2+%2B+80x+-+1200%29+