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tigry1 [53]
2 years ago
6

Based on the results from part C, which two statements correctly interpret actions the business should take? If material 2 is us

ed, Carrie will earn a profit if she sells chairs for more than $150 each. If material 1 is used, Carrie will earn a profit if she sells chairs for lower than $50 each. If material 3 is used, Carrie will earn a profit if she sells chairs between $45 and $160 each. If material 2 is used, Carrie will earn a profit if she sells chairs between $30 and $120 each. If material 1 is used, Carrie will earn a profit if she sells chairs between $40 and $70 each.
Mathematics
1 answer:
Serjik [45]2 years ago
6 0

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>

P(x) = 5000000- 20000x - 200000x + 2000x^2

P(x) = 5000000-220000x + 2000x^2

<u>Material 2</u>

P(x) = 4000000 - 10000x - 160000x+ 1000x^2

P(x) = 4000000-170000x+ 1000x^2

<u>Material 3</u>

P(x) = 2000000 - 5000x - 54000x - 270x^2

P(x) = 2000000 -59000x - 270x^2

Next, we test the options

Option 1: When material 2 is used

A price is greater than $150 is $151.

Calculate P(151) using P(x) = 4000000-170000x+ 1000x^2

So, we have:

P(151) = 4000000-170000 * 151+ 1000* 151^2

P(151) = 1131000

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 P(x) = 5000000-220000x + 2000x^2

So, we have:

P(49) = 5000000-220000 * 49 + 2000* 49^2

P(49) =-978000

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 P(x) = 2000000 -59000x - 270x^2

So, we have:

P(45) = 2000000 -59000 * 45 - 270 * 45^2

P(45) = -1201750

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 P(x) = 4000000-170000x+ 1000x^2

So, we have:

P(30) = 4000000-170000*30+ 1000*30^2

P(30) = -200000

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 P(x) = 5000000-220000x + 2000x^2

So, we have:

P(40) = 5000000-220000*40 + 2000*40^2

P(40) = -600000

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:

brainly.com/question/25638609

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