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The given function C models the total cost (sum of fixed cost and ... (May 2023 U.S.)
C(x)=50,000+0.75x
R(x)=4.75x
The given function C models the total cost (sum of fixed cost and variable cost), in dollars, of growing and harvesting x bales of hay on a certain farm.
The given function R models the revenue, in dollars, earned from selling x bales of hay.
16. According to the function R, how many bales of hay would have to be sold to earn a revenue of $1,425?
A) 100
B) 300
C) 500
D) 1,000
17. Which of the following inequalities models the number of bales of hay that must be sold to earn a profit of $10,000 or more? (profit = re cnue-cos t)
A) 10,000 ≤ 4x-50,000
B) 10,000 ≥ 4x-50,000
C) 10,000 ≤ 4x+50,000
D) 10,000 ≥ 4x+50,000
Solution
Correct answer: 16. B) 300
17. A) 10,000 ≤ 4x-50,000.
RESOLUTION QUESTION 16
To find the number of bales of hay needed to earn a revenue of $1,425, we'll use the revenue function:
R(x) = 4.75x
We know that R(x) = 1425, so we can set up the equation:
1425 = 4.75x
To solve for x, we divide both sides by 4.75:
x = 1425 / 4.75
Calculating this gives us:
x = 300
RESOLUTION QUESTION 17
Given:
C(x) = 50,000 + 0.75x (Total cost)
R(x) = 4.75x (Revenue)
Profit = Revenue - Cost
Goal:
Find the inequality representing the number of bales (x) to earn a profit of $10,000 or more.
Solution:
Express profit as an inequality:
Profit ≥ 10,000
R(x) - C(x) ≥ 10,000
Substitute the given functions:
4.75x - (50,000 + 0.75x) ≥ 10,000
Simplify the inequality:
4.75x - 50,000 - 0.75x ≥ 10,000
4x - 50,000 ≥ 10,000
Therefore, the correct inequality is:
A) 10,000 ≤ 4x - 50,000
Exam Edition: May 2023 U.S.
Exam Year: 2023
Related topics: Algebra, Applications and Modeling