the cost in dollars to produce x cups of lemonade is represented by the function c(x)=10 + 0.20x. the…

the cost in dollars to produce x cups of lemonade is represented by the function c(x)=10 + 0.20x. the revenue in dollars earned by selling x cups of lemonade is represented by the function r(x)=0.50x. what is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?\no 33 cups\no 33.33 cups\no 33.67 cups\no 34 cups

the cost in dollars to produce x cups of lemonade is represented by the function c(x)=10 + 0.20x. the revenue in dollars earned by selling x cups of lemonade is represented by the function r(x)=0.50x. what is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?\no 33 cups\no 33.33 cups\no 33.67 cups\no 34 cups

Answer

Explanation:

Step1: Set up inequality

We want $R(x)>C(x)$. So, $0.50x>10 + 0.20x$.

Step2: Subtract $0.20x$ from both sides

$0.50x-0.20x>10+0.20x - 0.20x$, which simplifies to $0.30x>10$.

Step3: Solve for $x$

$x>\frac{10}{0.30}=\frac{100}{3}\approx33.33$. Since $x$ represents the number of whole - cups, we take the next whole number.

Answer:

D. 34 cups