Question

Weenies is a food processing plant which manufactures hot dogs and hot dog buns. They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week. Each hot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of 800 pounds of pork product is delivered every Monday. Each hot dog requires ¼ pound of port product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each hot dog bun requires 2 minutes of labor. Each hot dog yields a profit of $0.80, and each bun yields a profit of $0.30. Weenies would like to know how many hot dogs and how many hot dog buns they should produce each week so as to achieve the highest possible profit. Formulate a linear programming model and solve it.

Answer 1

Answer : As per the given data

X1 = Number of hot dogs produced per week

X2 = Number of hot dog buns produced

profit P = 0.80 X1 + 0.30 X2

subjected to 0.1 X2  < 200 (flour)

1/4 X1 < 800 (pork)

3 X1 + 2 X2  < 5 * 40 * 60 (labor minute)

= 12000

X1 , X2  > 0

Number of hot dogs produced = 3200 and Number of hot dog buns produed = 1200 will give you highest profit of $2920