A cereal manufacturer makes two different kinds of cereal, Senior Citizen's Feast and Kids Go. Each pound of Senior Citizen's Feast requires 0.8 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 2880 lb of wheat, at most 850 lb of sugar, and at least 900 lb of the vitamin-enriched syrup. Let x represent the number of pounds of Senior Citizen's cereal and y represent the number of pounds of Kids Go cereal. Graph the region determined by the constraint inequalities.
A)
B)
C)
D)

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 0.8 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 2880 lb of wheat, at most 850 lb of sugar, and at least 900 lb of the vitamin-enriched syrup. Let x represent the number of pounds of Senior Citizen's cereal and y represent the number of pounds of Kids Go cereal. Graph the region determined by the constraint inequalities. ​
A)​ ​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

The constraint inequalities are:

0.8x + 0.4y ≤ 2880 (maximum amount of wheat)
0.2x + 0.2y + 0.2y ≥ 900 (minimum amount of vitamin-enriched syrup)
0.2y ≤ 850 (maximum amount of sugar)

We can graph each of these inequalities on the x-y plane:

- 0.8x + 0.4y ≤ 2880:

Solving for y:

y ≤ -2x + 7200

Plotting this line and shading below it:

A)​ 11eb0d3b_9800_25ac_9790_b9330e23eb59_TB1243_00

- 0.2x + 0.4y ≤ 850:

Solving for y:

y ≤ 0.5x + 2125

Plotting this line and shading below it:

B)​ 11eb0d3b_9800_25ad_9790_91e9c17bb61f_TB1243_00

- 0.2x + 0.4y + 0.2y ≥ 900:

Solving for y:

y ≥ -x + 4500

Plotting this line and shading above it:

C)​ 11eb0d3b_9800_25ae_9790_0fa001561f28_TB1243_00

The feasible region is the area that is shaded by all three inequalities:

D)​ 11eb0d3b_9800_25af_9790_534af7a05366_TB1243_00

E)​ 11eb0d3b_9800_25b0_9790_9d9536632a79_TB1243_00

The optimal solution is the point in the feasible region that maximizes the objective function. However, the objective function is not given in the problem statement, so we cannot find the optimal solution.

A Cereal Manufacturer Makes Two Different Kinds of Cereal, Senior