How to Maximize Profit for a Sausage Company

Maximizing Profit for a Sausage Company

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, while 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 a maximum of 1020 lb of beef, a maximum of 600 lb of pork, and at least 500 lb of spices.

Pounds of Hot Dogs to be Produced

Regular Hot Dogs: 2000 lbs

All-Beef Hot Dogs: 880 lbs

Maximum Profit

$3320 is the maximum profit that can be obtained.

Constraints and Optimization

Let x and y represent the weights of the regular and all-beef hot dogs produced, respectively. The task restrictions are as follows:

• 0.75x + 0.18y ≤ 1020 (limit on beef supply)
• 0.30y ≤ 600 (limit on pork supply)
• 0.2x + 0.2y ≥ 500 (limit on spice supply)

The goal is to maximize the profit p = 1.85x + 1.00y. The maximum profit is achieved at the point (x, y) = (880, 2000), as shown in the graph.

Conclusion

Producing 2000 pounds of regular hot dogs and 880 pounds of all-beef hot dogs will maximize profit, resulting in a total profit of $3320.