Question

A tent designer is working on a new tent. The tent will be made from black fabric, which costs $6 per yard, and green fabric, which costs $4 per yard. The designer will need at least 3 yards of black fabric, at least 4 yards of green fabric, and at least 10 yards of fabric overall. The total cost of the fabric used for the tent can be no more than $60. 1. Let x represent the number of yards of black fabric and y represent the number of yards of green fabric. Write the inequalities that model the four constraints in this situation. 2. Did you use a solid or dashed line for the boundary? Explain your choice. 3. Did you shade above or below the boundary line? Explain why. 4. Which ordered pair lies in the solution region that is common to all of inequalities? A) (2, 12) B) (4, 7) C) (6, 8) D) (10, 3)

Answer 1

Problem

A tent designer is working on a new tent. The tent will be made from black fabric, which costs $6 per yard, and green fabric, which costs $4 per yard. The designer will need at least 3 yards of black fabric, at least 4 yards of green fabric, and at least 10 yards of fabric overall. The total cost of the fabric used for the tent can be no more than $60.

Solution

Lets create some notation

x represent the number of yards of black fabric

y represent the number of yards of green fabric

From the ingo given we have this:

Part 1

x >= 3

y >= 4

x+ y >= 10

6x + 4y <= 60

Part 2

For this case we don't see any dashed line all the lines are defined and are solid

Part 3

For this case the first 3 inequalities are shaded above and the last one below

Part 4

the only point that asatisfy the conditions is

A) (2,12)