A sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.79 lb of beef and 0.24 lb of spices, and each pound of regular hot dogs requires 0.17 lb of beef, 0.34 lb of pork, and 0.22 lb of spices. Suppliers can deliver at most 1044 lb of beef, at most 402 lb of pork, and at least 300 lb of spices. Let x represent the number of pounds of regular meat and y represent the number of pounds of all beef. Graph the region determined by the constraint inequalities.
A)
B)
C)
D)
E)

Question

A sausage company makes two different kinds of hot dogs, regular and all beef. Each pound of all-beef hot dogs requires 0.79 lb of beef and 0.24 lb of spices, and each pound of regular hot dogs requires 0.17 lb of beef, 0.34 lb of pork, and 0.22 lb of spices. Suppliers can deliver at most 1044 lb of beef, at most 402 lb of pork, and at least 300 lb of spices. Let x represent the number of pounds of regular meat and y represent the number of pounds of all beef. Graph the region determined by the constraint inequalities. ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

Let x and y be the number of pounds of regular and all-beef hot dogs, respectively. Then, the constraints can be written as:

0.17x + 0.79y ≤ 1044   (beef constraint)
0.34x + 0.24y ≤ 300    (spice constraint)
0 ≤ x, y

To graph these constraints, we can plot the lines:

0.17x + 0.79y = 1044   (beef constraint)
0.34x + 0.24y = 300    (spice constraint)

and shade the region that satisfies all three constraints. The resulting graph is:

​ 11ea984b_ae01_e431_9029_8fc1f102aed1_TB4005_00

The feasible region is the shaded region, and the optimal solution occurs at the corner point (2400, 0), where we use only regular hot dogs. This is because the objective function (which we haven't been given in this problem) is linear and we want to maximize it, so we will always use as much of the cheaper ingredient (in this case, beef) as possible.

A Sausage Company Makes Two Different Kinds of Hot Dogs