Constrained Optimization: One Internal Binding Constraint Patz Company produces
ID: 341229 • Letter: C
Question
Constrained Optimization: One Internal Binding Constraint
Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $500 and $1,000, respectively. Assume initially that Patz can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 500 assembly hours per week.
Required:
1. Express the objective of maximizing the total contribution margin subject to the assembly-hour constraint.
Objective function: Max Z = $500 A + $1,000 B
Subject to: A + B
2. Identify the optimal amount that should be produced of each machine part. If none of the components should be produced, enter "0" for your answer.
Identify the total contribution margin associated with this mix.
$
3. What if market conditions are such that Patz can sell at most 125 units of Part A and 100 units of Part B? Express the objective function with its associated constraints for this case.
Objective function: Max Z = $500 A + $1,000 B
Identify the optimal mix and its associated total contribution margin.
$
Explanation / Answer
1.
Objective function: Max Z = $500 A + $1,000 B
Since, part A requires 2 hours of assembly & part B requires 5 hours of assembly, and there are only 500 hours available, hence: 2A + 5 B 500
2. Number of unit of part A that can be produced = 500/2= 250
Total contribution in this case = 250*500 = $1,25,000
Number of unit of part B that can be produced = 500/5=100
Total contribution in this case = 100*1000 = $1,00,000
Since, all that is prduced of either component can be sold, 250 units of part A should be produced where contribution would be $1,25,000
3.
Objective function: Max Z = $500 A + $1,000 B
B 100
Number of hours reqd to produce 125 units of part A = 125*2 = 250
Hence, hours left for part B = 250 wherein the number of parts that can be produced = 50
Hence, contibution at thiss level = 125*500+50*1000 = $1,12,500
Assembly-hour constraint 2A + 5 B 500 Demand constraint for Part A A 125 Demand constraint for Part BB 100