1. LP model Using
Excel & R

2. Product mix problem - Beaver Creek Pottery
Company
How many bowls and mugs should be
produced to maximize profits given labor and
materials constraints?

3.  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

4. Maximize Z = $40x1 + $50x2
subject to:
1x1 + 2x2 <= 40
4x1 + 3x2 <=120
x1, x2 >= 0

5. Maximize Z = $100x1 + $50x2
subject to:
1x1 + 2x2 <= 40
4x1 + 3x2 <= 120
x1, x2 >= 0

6. Maximize Z = $40x1 + $100x2
subject to:
1x1 + 2x2 <= 40
4x1 + 3x2 <= 120
x1, x2 >= 0

12. Using R