Linear Programming Model Set Objective Function
assembly lines. Assembly line 1 has 100 available hours, and assembly line 2
has 42 hours. Each product requires 10 hours of processing time on line 1,
while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The
profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.
a. Formulate a linear programming model for this problem.
2. The Pinewood Furniture Company produces chairs and tables
from two resources-labor and wood. The company has 80 hours of labor and 36
pounds of wood available each day. Demand for chairs is limited to 6 per day.
Each chair requires 8 hours of labor and 2 pounds of wood to produce, whereas a
table requires 10 hours of labour and 6 pounds of wood. The profit derived from
each chair is $400 and from each table, $100. The company wants to determine
the number of chairs and tables to produce each day in order to maximize
profit.
a. Formulate a linear programming model for this problem.
3. The Elixer Drug Company produces a drug from two
ingredients. Each ingredient contains the same three antibotics in different
proportions. One gram of ingredient 1 contributes 3 units, and ingredient 2
contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units
of antibiotic 2 are required, and the ingredients each contribute 1 unit per
gram. At least 12 units of abtibiotic 3 are required; a gram of ingredient 1
contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost
for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is
$50. The company wants to formulate a linear programming model to determine the
nunber of grams of each ingredient that must go into the drug in order to meet
the antibiotic requirements at the minimum cost.
a. Formulate a linear programming model for this problem.
4. A clothier makes coats and slacks. The two resources
required are wool cloth and labor. The clothier has 150 square yards of wool
and 200 hours of labor available. Each coat requires 3 square yards of wool and
10 hours of labor, whereas each pair of slacks requires 5 square yards of wool
and 4 hours of labor. The profit for a coat is $50, and the profit for slacks
is $40. The clothier wants to determine the number of coats and pairs of slacks
to make so that profit will be maximized.
a. Formulate a linear programming model for this problem.
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