A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.6 lb of wheat and 0.2 lb of vitamin-enriched syrup, and each pound of Kids Go requires 0.4 lb of wheat, 0.2 lb of sugar, and 0.2 lb of vitamin-enriched syrup. Suppliers can deliver at most 2800 lb of wheat, at most 800 lb of sugar, and at least 1000 lb of the vitamin-enriched syrup.

(a) Write the inequalities that describe how many pounds of each type of cereal can be made. (Let x represent the number of pounds of Senior Citizen's Feast, and let y represent the number of pounds of Kids Go.)

wheat constraint

vitamin-enriched syrup constraint

sugar constraint

x ≥ 0 pounds of Senior Citizen's Feast constraint

y ≥ 0 pounds of Kids Go constraint

(b) Graph the region determined by these constraint inequalities.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The first line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7000, passes through the point (2000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the second line, crosses the x-axis at approximately x = 4670, and exits the window in the fourth quadrant.

The second line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 5000, passes through the point (1000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the first line, crosses the x-axis at x = 5000, and exits the window in the fourth quadrant.

The third line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 4000, passes through the point (1000, 4000) crossing the second line, passes through the point (2000, 4000) crossing the first line, and exits the window in the first quadrant.

The region is above the first line, below the second line, and below the third line.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The first line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7000, passes through the point (2000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the second line, crosses the x-axis at approximately x = 4670, and exits the window in the fourth quadrant.

The second line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 5000, passes through the point (1000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the first line, crosses the x-axis at x = 5000, and exits the window in the fourth quadrant.

The third line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 4000, passes through the point (1000, 4000) crossing the second line, passes through the point (2000, 4000) crossing the first line, and exits the window in the first quadrant.

The region is above the first line, above the second line, below the third line, and above the x-axis.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The first line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7000, passes through the point (2000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the second line, crosses the x-axis at approximately x = 4670, and exits the window in the fourth quadrant.

The second line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 5000, passes through the point (1000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the first line, crosses the x-axis at x = 5000, and exits the window in the fourth quadrant.

The third line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 4000, passes through the point (1000, 4000) crossing the second line, passes through the point (2000, 4000) crossing the first line, and exits the window in the first quadrant.

The region is above the first line, above the third line, and right of the y-axis.

Question

A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.6 lb of wheat and 0.2 lb of vitamin-enriched syrup, and each pound of Kids Go requires 0.4 lb of wheat, 0.2 lb of sugar, and 0.2 lb of vitamin-enriched syrup. Suppliers can deliver at most 2800 lb of wheat, at most 800 lb of sugar, and at least 1000 lb of the vitamin-enriched syrup.

(a) Write the inequalities that describe how many pounds of each type of cereal can be made. (Let x represent the number of pounds of Senior Citizen's Feast, and let y represent the number of pounds of Kids Go.)

	wheat constraint
	vitamin-enriched syrup constraint
	sugar constraint
x ≥ 0	pounds of Senior Citizen's Feast constraint
y ≥ 0	pounds of Kids Go constraint

(b) Graph the region determined by these constraint inequalities.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The first line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7000, passes through the point (2000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the second line, crosses the x-axis at approximately x = 4670, and exits the window in the fourth quadrant.
The second line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 5000, passes through the point (1000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the first line, crosses the x-axis at x = 5000, and exits the window in the fourth quadrant.
The third line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 4000, passes through the point (1000, 4000) crossing the second line, passes through the point (2000, 4000) crossing the first line, and exits the window in the first quadrant.
The region is above the first line, below the second line, and below the third line.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The first line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7000, passes through the point (2000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the second line, crosses the x-axis at approximately x = 4670, and exits the window in the fourth quadrant.
The second line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 5000, passes through the point (1000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the first line, crosses the x-axis at x = 5000, and exits the window in the fourth quadrant.
The third line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 4000, passes through the point (1000, 4000) crossing the second line, passes through the point (2000, 4000) crossing the first line, and exits the window in the first quadrant.
The region is above the first line, above the second line, below the third line, and above the x-axis.

The x y-coordinate plane is given. There are 3 lines and a region on the graph.

The first line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 7000, passes through the point (2000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the second line, crosses the x-axis at approximately x = 4670, and exits the window in the fourth quadrant.
The second line enters the window in the second quadrant, goes down and right, crosses the y-axis at y = 5000, passes through the point (1000, 4000) crossing the third line, passes through the point (4000, 1000) crossing the first line, crosses the x-axis at x = 5000, and exits the window in the fourth quadrant.
The third line enters the window in the second quadrant, goes horizontally right, crosses the y-axis at y = 4000, passes through the point (1000, 4000) crossing the second line, passes through the point (2000, 4000) crossing the first line, and exits the window in the first quadrant.
The region is above the first line, above the third line, and right of the y-axis.

Accepted Answer

Answered: Image /qna-images/answer/d0d031f9-d24d-4457-93dd-2cfd62a317c5.jpg