👤
Answered

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

Answer :

MrRoyalgo

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.

How to determine the true profit functions

From the complete questions, the profit functions are calculated as follows:

Material 1

[tex]P(x) = 5000000- 20000x - 200000x + 2000x^2[/tex]

[tex]P(x) = 5000000-220000x + 2000x^2[/tex]

Material 2

[tex]P(x) = 4000000 - 10000x - 160000x+ 1000x^2[/tex]

[tex]P(x) = 4000000-170000x+ 1000x^2[/tex]

Material 3

[tex]P(x) = 2000000 - 5000x - 54000x - 270x^2[/tex]

[tex]P(x) = 2000000 -59000x - 270x^2[/tex]

Next, we test the options

Option 1: When material 2 is used

A price is greater than $150 is $151.

Calculate P(151) using [tex]P(x) = 4000000-170000x+ 1000x^2[/tex]

So, we have:

[tex]P(151) = 4000000-170000 * 151+ 1000* 151^2[/tex]

[tex]P(151) = 1131000[/tex]

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 [tex]P(x) = 5000000-220000x + 2000x^2[/tex]

So, we have:

[tex]P(49) = 5000000-220000 * 49 + 2000* 49^2[/tex]

[tex]P(49) =-978000[/tex]

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 [tex]P(x) = 2000000 -59000x - 270x^2[/tex]

So, we have:

[tex]P(45) = 2000000 -59000 * 45 - 270 * 45^2[/tex]

[tex]P(45) = -1201750[/tex]

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 [tex]P(x) = 4000000-170000x+ 1000x^2[/tex]

So, we have:

[tex]P(30) = 4000000-170000*30+ 1000*30^2[/tex]

[tex]P(30) = -200000[/tex]

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 [tex]P(x) = 5000000-220000x + 2000x^2[/tex]

So, we have:

[tex]P(40) = 5000000-220000*40 + 2000*40^2[/tex]

[tex]P(40) = -600000[/tex]

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:

https://brainly.com/question/25638609

Go Teaching: Other Questions