Question

Bernice is a furniture maker who specializes in creating dining tables out of recycled material. Her total profit from these tables, p, is represented as a function of the number of dining tables sold, s. Each table costs $300.00. For every standard dining table she makes, she uses 8 recycled wall studs. She has 200 recycled wall studs on hand.

Bernice wants to estimate her possible profit based on the materials she has on hand.

What are the domain and range of P(s), Bernice’s profit? How do you know this?

Select the option that correctly answers both questions.

A. Because Bernice has 200 wall studs on hand, she can fulfill 25 table orders at most. She can sell between 0 and 25 tables, and thus the range is [0,25]. Bernice’s profit is a function of the number of tables sold. Since she can sell as few as 0 tables, her minimum profit is $0. And, since she can sell as many as 25 tables at $300 each, her maximum profit is $7500. Thus, the domain is [0,7500].

B. Because Bernice has 200 wall studs on hand, she can fulfill 25 table orders at most. She can sell between 0 and 25 tables, and thus the domain is (0,25). Bernice’s profit is a function of the number of tables sold. Since she can sell as few as 0 tables, her minimum profit is $0. And, since she can sell as many as 25 tables at $300 each, her maximum profit is $7500. Thus the range is (0,7500).

C. Because Bernice has 200 wall studs on hand, she can fulfill 25 table orders at most. She can sell between 0 and 25 tables, and thus the domain is [0,25]. Bernice’s profit is a function of the number of tables sold. Since she can sell as few as 0 tables, her minimum profit is $0. And, since she can sell as many as 25 tables at $300 each, her maximum profit is $7500. Thus, the range is [0,7500].

D. Theoretically, Bernice can sell as many tables as are ordered, and thus the domain is [0,∞). If she can make infinitely many dining tables, she will make an infinite amount of money, and thus the range is [0,∞).

Answer 1

Answer: The answer is (C).

Step-by-step explanation: Given that Bernice is a furniture maker and specialises in creating dining tables out of recycled material. The total profit she makes is represented by 'p', which is a function of the number of dining tables sold.

The cost of each dining table is $300. For each dining table, she uses 8 recycled wall studs and since she has 200 recycled wall studs available, so the maximum number of tables she can make is

`n=(200)/(25)=25.`

So, the domain is [0, 25].

Also, since the cost of each dining table is $300, so the maximum profit she can make is

`p=\$(300* n)=\$(300* 25)\$7500.`

So, the range is [0, 7500].

Thus, the correct option is (C).