The document describes a linear programming problem to determine the optimal product mix for Beaver Creek Pottery Company to maximize daily profits given constraints on labor hours and materials. The objective is to maximize total profit (Z) from bowls ($40 each) and mugs ($50 each). The constraints are that bowl production uses 1 labor hour and 4 pounds of clay each, while mug production uses 2 labor hours and 3 pounds of clay each, with no more than 40 labor hours or 120 pounds of clay available per day. The complete linear programming model is defined to maximize profit Z subject to the constraints.
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. ï‚— Step 1: define decision variables
ï‚— Let x1=number of bowls to produce/day
ï‚— x2= number of mugs to produce/day
ï‚— Step 2: define the objective function
ï‚— maximize Z = $40x1 + 50x2
ï‚— where Z= profit per day
ï‚— Step 3: state all the resource constraints
ï‚—
ï‚— constraint 1) 1x1 + 2x2 <= 40 hours of labor ( resource
ï‚— constraint 2) 4x1 + 3x2 <= 120 pounds of clay
(resource
ï‚— Step 4: define non-negativity constraints
ï‚— x1>=0; x2 >= 0
ï‚— Complete Linear Programming Model:
ï‚— maximize Z=$40x1 + 50x2
ï‚— subject to
ï‚— 1x1 + 2x2 <= 40
ï‚— 4x2 + 3x2 <= 120
ï‚— x1, x2 >= 0
