SOLUTION: Question: It costs $0.30 for Tina to produce a glass of lemonade. If she charges p dollars for one glass, she believes she can sell 50 - p glasses of lemonade in a day. Find a quad

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Question: It costs $0.30 for Tina to produce a glass of lemonade. If she charges p dollars for one glass, she believes she can sell 50 - p glasses of lemonade in a day. Find a quad      Log On


   

Question 1044895: Question: It costs $0.30 for Tina to produce a glass of lemonade. If she charges p dollars for one glass, she believes she can sell 50 - p glasses of lemonade in a day. Find a quadratic function that gives Tina's daily profit as a function of price. Then graph Tina's profit as a function of price.
Answer: This is as far as I got - any help appreciated.
I thought if X = glasses sold then X = (50-p). And Profit would be the price of one glass (p) - 0.30, then Total Profit would be = (50-p)(p-0.30). I then tried to use algebra to simplify this, and think I came unstuck. I used the FOIL method (first, outer, inner, last). So F (50 * p) = 50P. O (50*-0.30) = - 15. I (-p * p) = -p^2. L (-p*-0.30) = 3P/10. So the final equation would be -p^2 + 50p - 3P/10 - 15. I then got lost as to how to simplify 50p - 3p/10. Thanks in advance.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
DAILY PROFIT is (number of glasses)*(price)-(cost of 1 glass)*(number of glasses)

OR

p%2850-p%29-%280.3%29%28p%29, using p for price; compare to the description and then try simplifying.

If you choose y as the profit, then highlight_green%28y=p%2850-p%29-0.3p%29.
Remember, you chose x, which I am now choosing as the lower-case form, for number of glasses lemonade sold. If x is number of glasses sold, and 50-p glasses expected to be sold, then 50-p=x.

y=50p-p%5E2-0.3p
y=-p%5E2-0.3p%2B50p
y=-p%5E2%2B49.7p
More easily used factored,
y=-p%28p%2B49.7%29
highlight%28y=p%2849.7-p%29%29--------a parabola with a maximum value, which occurs in exact middle of 0 and 49.7. You will want the nearest whole number to this middle value of p.