Question

1.

Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, i, which costs $4 a bottle, and new brushes, b, which are $15 each. Which inequality below represents this scenario?

4i + 100 15b

15i + 4b 100

4i + 15b 100

15i + 4b 100
2.
Jon owns a clothing store where he designs pairs of shorts, s, and T-shirts, t. He sells shorts for $14 and T-shirts for $6 each. Jon can work 12 hours a day, at most. It takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts. He must design at least 12 items each day, but he cannot design more than 20 items in one day. Write 5 inequalities that represent the explicit and assumed constraints in the problem.(Hint... change times to hours)
3.
John owns a clothing store that sells shorts and graphic T-shirts. He sells the shorts for $12 each and T-shirts for $5 each. He is limited to the constraints shown by the set of inequalities below. Which of the points (s, t) will maximize John's revenue? Show all work to get full credit! (Hint... start by finding the profit function)

s<10 - 0.5t
s>5-t
s<20-t
s>0
t>0
4.
Phoebe owns a clothing store that designs T-shirts and shorts. She sells the T-shirts for $5 each and the shorts for $16 each. She can work 12 hours a day at most. It takes her 15 minutes to design a T-shirt and 30 minutes to design a pair of shorts. She must design at least 15 items a day, but cannot design more than 25 items in a day. Which of the values below is the maximum revenue Phoebe can make with these constraints? (Hint... start by finding the revenue function)
5.
A clothing design company pays two different people to design its T-shirts. The company pays person A $8 an hour and pays person B $12. Person A cannot work more than twice as many hours as person B, but they cannot work more than 20 hours total. Person A makes the company a profit of $10 an hour, and person B makes the company a profit of $20 an hour. If the company wants to make at least $150 in profit, what value will minimize the cost to the company? Show all work to get full credit.

Answer 1

Explanation:

1) In the current situation, the total amount is $100 and the cost of an ink bottle is $4.Whereas, the cost of each brush is $15.She cannot spend more than $100.

The equation which best describes the situation is:

4i + 15b ≤ 100

2) He sells shorts for $14 and T-shirts for $6 each

14s + 6t

3) It takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts.

0.15t + 1s ≤ 12

4) He must design at least 12 items each day

s + t ≥ 12

5) He cannot design more than 20 items in one day.

s + t ≤20

Answer 2

Q1. Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, I, which costs $4 a bottle, and new brushes, b, which are $15 each.

Solution:
In the current situation, the total amount is $100 and the cost of an ink bottle is $4.Whereas, the cost of each brush is $15.She cannot spend more than $100.

Therefore,
The equation which best describes the situation is:
4i + 15b ≤ 100

Q.2 Jon owns a clothing store where he designs pairs of shorts, s, and T-shirts, t. He sells shorts for $14 and T-shirts for $6 each. Jon can work 12 hours a day, at most. It takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts. He must design at least 12 items each day, but he cannot design more than 20 items in one day. Write 5 inequalities that represent the explicit and assumed constraints in the problem.

Solution:
He sells shorts for $14 and T-shirts for $6 each
14s + 6t

It takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts.
0.15t + 1s ≤ 12

He must design at least 12 items each day
s + t ≥ 12

he cannot design more than 20 items in one day.
s + t ≤20