Using the Simplex Method...
1.) maximize x + 2y subject to the constraints
-x + y ≤ 100
6x + 6y ≤ 1200
x ≥ 0; y ≥ 0
2.) maximize 3x + 2y + 5z subject to the constraints
x + 2z ≤ 10
3y + 2z ≤ 24
x ≥ 0; y ≥ 0
3.) suppose that a furniture manufacturer makes chairs, sofas and tables. the amounts of labour of various types as well as the relative availability of each type are summarized by the following chart:
chair sofa table daily labour available (hrs.)
carpentry 6 3 8 768
finishing 1 1 2 144
upholstery 2 5 216
The profit per chair is $80, per sofa is $70 and per tableis $120. How many pieces of each type of furniture should be manufactured each day to maximize profit?
4.) minimize 3x + 5y + z , subject to the constraints
x + y + z ≥ 20
y + 2z ≥ 20
x ≥ 0; y ≥ 0; z ≥ 0
5.) a dietician is designing a daily diet that is to contain at least 60 units of protein, 40 units of carbohydrates and 120 units of fat. The diet is to cnsit of two types of foods. One serving of food-A contains 30 units of protein, 10 units of carbohydrates, and 20 units of fat and costs $3. One serving of food-B contains 10 units of protein, 10 units of carbohydrates and 60 units of fat and costs $1.50. Design the diet that provides the daily requirements at the least cost.