Happy Planet drinks price change as the quantity sold changes. In particular p=19-0.005x. The total cost to produce the drinks are $5 per drink. Their productio

Question

Happy Planet drinks price change as the quantity sold changes. In particular p=19-0.005x. The total cost to produce the drinks are $5 per drink. Their production factory costs $1903 per month. What is the profit maximum?

Answer 1

Max profit at 1400 drinks sold = $7,897

revenue=$16,800 Variable cost =$7,000  fixed cost $1903   Net $7,897

Price $12/ drink

Answer 2

Dylan,

 

According to this problem each drink generates 19-.005x and costs 5 so total profit is 19x-.005x^2-5x-1903 or

-.005x^2+14x-1903. We differentiate this to find the maximum point: -.01x+14=0 so x=140 drinks.

 

At 140 drinks, price p is 18.3 and cost is 5 so profit per drink is 13.3, totaling 1862 less production cost (1903)=-41.

 

Hope that helps!