section 4.2 mth 1310 web assign finite math

Question

A sausage company makes two different kinds of hot dogs, regular and all-beef. Each pound of all-beef hot dogs requires 0.75 lb of beef and 0.2 lb of spices, and each pound of regular hot dogs requires 0.18 lb of beef, 0.3 lb of pork, and 0.2 lb of spices. Suppliers can deliver at most 1020 lb of beef, at most 600 lb of pork, and at least 500 lb of spices. If the profit is $1.55 on each pound of all-beef hot dogs and $1.00 on each pound of regular hot dogs, how many pounds of each should be produced to obtain maximum profit?

regular hot dogs
all-beef hot dogs

What is the maximum profit?

$  

Answer 1

Lets let B represent the number of all beef hotdogs and R represent the number of regular hot dogs. So when you make your constraints, then the total beef used in the hot dogs is 0.75B+0.18R, the total pork used is 0.3R, and the total spices used is 0.2B+0.2R. This makes your constraints as follows:

0.75B + 0.18R ≤ 1020

0.3R ≤ 600

0.2B + 0.2R ≥ 500

And the function that you're maximizing is 1.55B + 1R.

Sketch the region and find the corner points. I've found them to be (B, R) = (500, 2000), (880,2000), and (1000, 1500). Check which makes the largest function value (you can skip the first point as the second point is obviously larger than it).

1.55(880) + 2000 = 3364

1.55(1000) + 1500 = 3050

So 880 all beef hot dogs and 2000 regular hot dogs maximizes your profit at $3364 dollars.