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 $1.50 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

Answer:

• 880 lbs of all-beef hot dogs
• 2000 lbs of regular hot dogs
• maximum profit is $3320

Step-by-step explanation:

We can let x and y represent the number of pounds of all-beef and regular hot dogs produced, respectively. Then the problem constraints are ...

• .75x + 0.18y ≤ 1020 . . . . . . limit on beef supply
• .30y ≤ 600 . . . . . . . . . . . . . limit on pork supply
• .2x + .2y ≥ 500 . . . . . . . . . . limit on spice supply

And the objective is to maximize

  p = 1.50x + 1.00y

The graph shows the constraints, and that the profit is maximized at the point (x, y) = (880, 2000).

2000 pounds of regular and 880 pounds of all-beef hot dogs should be produced. The associated maximum profit is $3320.