LP model Using

Excel & R

Product mix problem - Beaver Creek Pottery Company

How many bowls and mugs should be produced to maximize profits given labor and materials constraints?

Step 1: define decision variables Let x1=number of bowls to produce/day x2= number of mugs to produce/day Step 2: define the objective function maximize Z = $40x1 + 50x2

where Z= profit per day Step 3: state all the resource constraints constraint 1) 1x1 + 2x2 <= 40 hours of labor ( resource constraint 2) 4x1 + 3x2 <= 120 pounds of clay (resource

Step 4: define non-negativity constraints x1>=0; x2 >= 0

Complete Linear Programming Model:

maximize Z=$40x1 + 50x2

subject to 1x1 + 2x2 <= 40 4x2 + 3x2 <= 120 x1, x2 >= 0

Maximize Z = $40x1 + $50x2

subject to: 1x1 + 2x2 <= 40

4x1 + 3x2 <=120 x1, x2 >= 0

Maximize Z = $100x1 + $50x2

subject to: 1x1 + 2x2 <= 40

4x1 + 3x2 <= 120 x1, x2 >= 0

Maximize Z = $40x1 + $100x2

subject to : 1x1 + 2x2 <= 40

4x1 + 3x2 <= 120 x1, x2 >= 0

Using R