Certified Management Accountant Decision Analysis 4 — Questions and Answers
Question 1: When a single production constraint exists, the optimal product mix is determined by ranking products according to:
- Highest unit selling price
- Highest total revenue potential
- Highest contribution margin per unit of the constrained resource (Correct answer)
- Highest gross profit percentage
Correct answer: Highest contribution margin per unit of the constrained resource
With one binding constraint, maximizing contribution margin per unit of that constrained resource (e.g., machine hours) yields the optimal mix.
Question 2: Product X yields $6 CM and requires 2 machine hours. Product Y yields $4 CM and requires 1 machine hour. Machine capacity is limited. Which product should be prioritized?
- X; it has the higher CM per unit ($6 > $4)
- Y; it requires fewer machine hours
- Y; its CM per machine hour ($4) exceeds X's CM per machine hour ($3) (Correct answer)
- X; it generates more total revenue
Correct answer: Y; its CM per machine hour ($4) exceeds X's CM per machine hour ($3)
CM per machine hour: X = $6/2 = $3; Y = $4/1 = $4; Product Y is more profitable per constrained resource.
Question 3: In a linear programming model for product mix, the 'feasible region' is defined as:
- The single point that maximizes the objective function
- The set of all variable combinations satisfying all constraints simultaneously (Correct answer)
- The region where all constraints are violated
- The line connecting the two most profitable products
Correct answer: The set of all variable combinations satisfying all constraints simultaneously
The feasible region is the solution space where every constraint (resource, demand, non-negativity) is satisfied at the same time.
Question 4: The shadow price (dual value) of a binding constraint in linear programming represents:
- The cost to purchase one additional unit of the constrained resource
- The increase in the optimal objective function value from one additional unit of the binding constraint (Correct answer)
- The selling price of the scarce resource
- The reduction in variable cost from relaxing the constraint
Correct answer: The increase in the optimal objective function value from one additional unit of the binding constraint
Shadow price measures how much the objective function (e.g., total contribution margin) would improve with one additional unit of the binding resource.
Question 5: A company produces three products competing for a bottleneck machine. Product A: CM $20, 4 hrs. Product B: CM $15, 2 hrs. Product C: CM $18, 3 hrs. The optimal ranking is:
- A, C, B (by total CM descending)
- B, C, A (by CM per bottleneck hour descending) (Correct answer)
- C, A, B (by CM per bottleneck hour descending)
- A, B, C (by highest selling price)
Correct answer: B, C, A (by CM per bottleneck hour descending)
CM/hr: A = $5, B = $7.50, C = $6; ranking by CM per bottleneck hour gives B ($7.50), C ($6), A ($5).
Question 6: When slack variables in a linear programming solution are greater than zero, this indicates the associated constraint is:
- Binding and limiting output
- Non-binding with unused capacity remaining (Correct answer)
- Infeasible and must be removed
- The active constraint driving the optimal solution
Correct answer: Non-binding with unused capacity remaining
A positive slack variable means the constraint is not fully utilized; resources are available beyond what the optimal solution requires.
Question 7: A company introduces a second binding constraint in addition to machine hours. Compared to a single-constraint model, the optimal solution will:
- Always increase total contribution margin
- Remain unchanged because constraints are additive
- Equal or decrease total contribution margin as the feasible region shrinks (Correct answer)
- Shift to maximizing revenue instead of contribution margin
Correct answer: Equal or decrease total contribution margin as the feasible region shrinks
Adding a constraint tightens or maintains the feasible region; the optimal objective function value can only stay the same or worsen (decrease).
Certified Management Accountant Decision Analysis 4
When a single production constraint exists, the optimal product mix is determined by ranking products according to: