Math Problem Statement
Neptune Company has developed a small inflatable toy that it is anxious to introduce to its customers. The company’s Marketing Department estimates that demand for the new toy will range between 10,000 units and 35,000 units per month. The new toy will sell for $9.00 per unit. Enough capacity exists in the company’s plant to produce 15,000 units of the toy each month. Variable expenses to manufacture and sell one unit would be $5.00 , and incremental fixed expenses associated with the toy would total $32,000 per month.
Neptune has also identified an outside supplier who could produce the toy for a price of $4.00 per unit plus a fixed fee of $29,000 per month for any production volume up to 15,000 units. For a production volume between 15,001 and 35,000 units the fixed fee would increase to a total of $58,000 per month.
Required: Calculate the break-even point in unit sales assuming that Neptune does not hire the outside supplier. Note: Do not round your intermediate calculations.
How much profit will Neptune earn assuming:
- It produces and sells 15,000 units.
- It does not produce any units and instead outsources the production of 15,000 units to the outside supplier and then sells those units to its customers.
- Calculate the break-even point in unit sales assuming that Neptune plans to use all of its production capacity to produce the first 15,000 units that it sells and that it also commits to hiring the outside supplier to produce up to 20,000 additional units.
- Assume that Neptune plans to use all of its production capacity to produce the first 15,000 units that it sells and that it also commits to hiring the outside supplier to produce up to 20,000 additional units. a. What total unit sales would Neptune need to achieve in order to equal the profit earned in requirement 2a? b. What total unit sales would Neptune need to achieve in order to attain a target profit of $30,500 per month? c. How much profit will Neptune earn if it sells 35,000 units per month? d. How much profit will Neptune earn if it sells 35,000 units per month and agrees to pay its marketing manager a bonus of 20 cents for each unit sold above the break-even point from requirement 3?
Solution
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Math Problem Analysis
Mathematical Concepts
Break-even analysis
Cost-benefit analysis
Profit calculation
Production cost management
Formulas
Break-even point (in units) = Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)
Profit = Sales Revenue - Variable Costs - Fixed Costs
Outsourced Profit = Sales Revenue - (Variable Costs from Supplier + Supplier Fixed Costs)
Theorems
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Suitable Grade Level
College level, Business or Economics
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