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?\n33 cups\n33.33 cups\n33.67 cups\n34 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?\n33 cups\n33.33 cups\n33.67 cups\n34 cups

Answer

Explanation:

Step1: Set up the inequality

We want $R(x)>C(x)$. Given $C(x) = 10 + 0.20x$ and $R(x)=0.50x$, the inequality is $0.50x>10 + 0.20x$.

Step2: Solve the inequality for x

Subtract $0.20x$ from both sides: $0.50x-0.20x>10+0.20x - 0.20x$ $0.30x>10$. Then divide both sides by $0.30$: $x>\frac{10}{0.30}=\frac{100}{3}\approx33.33$.

Step3: Find the minimum whole - number value of x

Since $x$ represents the number of whole cups and $x > 33.33$, the minimum value of $x$ is 34.

Answer:

D. 34 cups