Algebra 1 math help

Question

It costs a company $20 per box to make pocket-sized stuffed animals. The company also has a fixed manufacturing cost of $2300. The owners are trying to calculate their cost for making boxes of animals.

1. Identify the variables in this relationship and indicate which would be the independent variable and which would be the dependent variable.
2. Complete the table to explore this relationship. Then, use the table to write a function rule that describes the relationship between the number of boxes manufactured, b, and the cost of manufacturing those boxes, c.

Number of boxes	(b)	Process	Manufacturing cost	in dollars (c)
0
1
2
10
50
100
b

1. How much does it cost to manufacture 300 boxes of stuffed animals? Explain or show how you found your solution.
2. How many boxes of stuffed animals can the company manufacture for $5000? Explain or show how you found your solution.

 

1. Is this situation a function? Why or why not?  

 

1. Explain what the point (135, 5000) means in context of this situation.

Answer 1

The variables are the number of boxes (independent) and the cost of manufacturing the boxes (dependent).

c = 20b + 2300, where b is the number of boxes and c is the cost of manufacturing the boxes

b = 0: 20(0) + 2300 = 0 + 2300 = 2300 → c = 2300

b = 1: 20(1) + 2300 = 20 + 2300 = 2320 → c = 2320

b = 2: 20(2) + 2300 = 40 + 2300 = 2340 → c = 2340

b = 10: 20(10) + 2300 = 200 + 2300 = 2500 → c = 2500

b = 50: 20(50) + 2300 = 1000 + 2300 = 3300 → c = 3300

b = 100: 20(100) + 2300 = 2000 + 2300 = 4300 → c = 4300

b = 300: 20(300) + 2300 = 6000 + 2300 = 8300 → c = 8300

The cost of manufacturing 300 boxes is $8,300.

20b + 2300 = 5000

20b = 2700

b = 135

The company will pay $5,000 for manufacturing 135 boxes of stuffed animals. The solution point will look like (135, 5000).

This situation will be the function. The cost of manufacturing boxes depends on the number of boxes that can be produced → c(b) = 20b + 2300.