Question

A meat packing company makes pork sausage in 1,000 pound batches. The sausages are made from pork, beef, and filler. The cost of pork is $4.00 per pound, the cost of beef is $3.00 per pound, and the cost of filler is $2.00 per pound. Each batch must contain the following:

(I)   At least 30 percent pork.

(ii) No more than 20 percent filler.

(iii) At least 200 pounds of beef.

(iv) At least two pounds of pork for every pound of filler

The manager wants to know the mix of ingredients that will minimize cost. Formulate an LP model for this problem.

Answer 1

Let the number of pounds of pork be x

Let the number of pounds of beef be y

Let the number of pounds of filler be z

Minimize, Cost = 4.00*x + 3.00*y + 2.00*z

Constraints:

x + y + z = 1000 [Batch size must be of 1000]

x >= 0.3(x+y+z) [At least 30 percent pork]

y <= 0.2(x+y+z) [No more than 20 percent filler]

y >= 200 [At least 200 pounds of beef]

x >= 2*z [At least two pounds of pork for every pound of filler]

So, the minima exists when

x = 533.33 pounds, y = 200 pounds and z = 266.67 pounds

Minimal Cost = 3266.67 pounds

Note - Post any doubts/queries in comments section.