A wholesale distributor of packaged nuts sells two different mixes of peanuts and cashews, mix A and mix B. Each package of mix A nuts contains 8 ounces (oz.) of peanuts and 4 oz. of cashews. Each package of mix B nuts contains 6 oz. of peanuts and 6 oz. of cashews. Let x represent the number of packages of mix A nuts and let y represent the number of packages of mix B nuts. No more than 120 oz. of peanuts and no more than 96 oz. of cashews can be used each day. Which graph represents the numbers of packages of mix A and mix B that can be produced?

The answer is below

Step-by-step explanation:

Let x represent the number of packages of mix A nuts and let y represent the number of packages of mix B nuts

Since 8 ounces (oz.) of peanuts is used to produce a package of mix A and 6 ounces (oz.) of peanuts is used to produce a package of mix B. Also, No more than 120 oz. of peanuts can be used each day. This can be represented by the inequality:

8x + 6y ≤ 120             (1)

4 ounces (oz.) of cashew is used to produce a package of mix A and 6 ounces (oz.) of cashew is used to produce a package of mix B. Also, No more than 96 oz. of peanuts can be used each day. This can be represented by the inequality:

4x + 6y ≤ 96            (2)

The inequality from equation 1 and equation 2 is graphed using geogebra online graphing.

If x, y ≥ 0, the solution to the problem is:

(0, 0), (0, 16), (15,0), (6, 12)