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The profit function is the difference between the cost and the revenue functions.
The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.
<h3>How to determine the true profit functions</h3>From the complete questions, the profit functions are calculated as follows:
<u>Material 1</u>
<u>Material 2</u>
<u>Material 3</u>
Next, we test the options
Option 1: When material 2 is used
A price is greater than $150 is $151.
Calculate P(151) using
So, we have:
P(151) is greater than 0; this represents a profit
Hence, option (1) is true
Option 2: When material 1 is used
A price is less than $50 is $49.
Calculate P(49) using
So, we have:
P(49) is less than 0; this represents loss
Hence, option (2) is false
Option 3: When material 3 is used
Calculate P(45) and P(160) using
So, we have:
P(45) is less than 0; this represents loss
Hence, option (3) is false
Option 1: When material 2 is used
Calculate P(30) and P(120) using
So, we have:
P(30) is less than 0; this represents a loss
Hence, option (4) is false
Option 2: When material 1 is used
Calculate P(40) and P(70) using
So, we have:
P(49) is less than 0; this represents loss
Hence, option (5) is false
The above means that:
The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.
Read more about revenue functions at: