Originally Posted by
Angie80 Here is a problem I am working on...
Ann is staring up her lemonade stand. Number of glasses of lemonade sold per day is a function of sale price p=p(x), where x is the price.
She notices that 75 glasses of lemonade were sold at 60 cents, but only 45 at 80 cents. If number of glasses sold is a linear function of sale price, what should p(x) be?
So, I came up with the solution:
Linear function p(x) = -3/2x +165
and now:
The gross profit f(x) of her lemonade stand is equal to the number of glasses sold, multiplied by sale price. It costs 20 cents to get the ingredients for one glass of lemonade. It also costs 2 dollars a day to keep her brother from interfering with the business.
Sketch the gross profit f(x) and the overhead (as function of price) on the same graph. Find an expression for the net profit expressed as a function of the price.
I came up with something like this:
gross profit
f(x) = p(x)(x)
f(x) = (-3/2x +165 )x= -3/2x^2 + 165x
Net profit g(x)= -3/2x^2 +195x-3500
And now, at what price should lemonade be sold to make any profit at all??