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)
E)

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) ​ 
E) ​

Quizplus · Accepted Answer

The constraints are:

0.8x + 0.4y ≤ 2880 (wheat constraint)
0.2x + 0.2y + 0.2y ≥ 900 (vitamin-enriched syrup constraint)
0.2y ≤ 850 (sugar constraint)

Simplifying the vitamin-enriched syrup constraint gives:

0.4x + y ≥ 450

Plotting these constraints on a graph gives:

A) is incorrect because it does not include the vitamin-enriched syrup constraint.
B) is incorrect because it does not include the sugar constraint.
C) is the correct answer because it includes all three constraints and the feasible region is shaded.
D) is incorrect because it includes the wrong wheat constraint (should be 0.8x + 0.4y ≤ 2880 not 0.8x + 0.2y ≤ 2880).
E) is incorrect because it does not include the vitamin-enriched syrup constraint.

A Cereal Manufacturer Makes Two Different Kinds of Cereal, Senior