Subjects business math

Contribution Margin Drop 61C428

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to find how much the contribution margin per unit can drop before the business should shut down in the short run. 2. **Define contribution margin:** Contribution margin per unit is the selling price per unit minus the variable cost per unit. 3. **Given data:** - Selling price per unit $P = 64.6$ - Cost to produce per unit (variable cost) $VC = 24.32$ - Fixed costs $FC = 1101$ - Anticipated units sold $Q = 625$ 4. **Calculate current contribution margin per unit:** $$CM = P - VC = 64.6 - 24.32 = 40.28$$ 5. **Calculate total contribution margin:** $$Total\ CM = CM \times Q = 40.28 \times 625 = 25175$$ 6. **Determine shutdown point:** The business should shut down if total contribution margin is less than fixed costs, i.e., $$Total\ CM < FC$$ 7. **Find minimum contribution margin per unit to cover fixed costs:** $$CM_{min} \times Q = FC$$ $$CM_{min} = \frac{FC}{Q} = \frac{1101}{625} = 1.7616$$ 8. **Calculate how much contribution margin can drop:** $$Drop = CM - CM_{min} = 40.28 - 1.7616 = 38.5184$$ **Final answer:** The contribution margin per unit can drop by approximately $38.52$ before the business should shut down in the short run.