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Math and Science Solutions for Businesses/What do I do to get net sale?


What do I do to get net sale, please show work?

50 percent (net sales) = $85,000 + 30.5 percent (net sales)
Net sales = ?

50 percent (net sales) = $87,000 + 28.2 percent (net sales)
Net sales = ?

Here is more info:
Assume that you own a sandwich shop. In looking over last year's income statement you see that the annual sales were $250,000 with a gross margin of 50 percent, or $125,000. The fixed operating expenses were $50,000: the variable operating expenses were 20 percent of sales, or $50,000: and your profit was $25,000, or 10 percent of sales.
In discussions with your spouse, you wonder if joining a franchise operation such as Subway or Blimpie would improve your results. Your research has determined that Subway requires a $37,500 licensing fee in addition to an 4-percent royalty on sales and a 4.2-percent advertising fee on sales. Blimpie, while requiring an $35,000 licensing fee, charges only a 6-percent royalty and a 4.5-percent advertising fee.

Assuming that you wanted to break-even, what amount of sales would you have to generate with each channel during the first year, since both your fixed and variable expenses would increase?
Remember the break-even point (BEP) is where gross margin equals total operating expenses: in equation form, this is:
Gross Margin =Fixed Operating Expenses + Variable Operating Expenses
Thus, with Subway, fixed expenses would increase from $50,000 to $87,000 and your variable expenses would increase from 20 percent of sales to 28.2 percent (20 percent + 4 percent + 4.2 percent). Blimpie's would increase fixed expenses by $35,000 and variable expenses by 10.5 percent.

To answer the first part of your question, let

N = net sales

so that, for the first expression

50 percent (net sales) = $85,000 + 30.5 percent (net sales) => 0.5N = 85000 + 0.305N

or, using a little algebra

N = $85000/(0.5-0.305) = $105,590

and for the second expression

N = $87000/(0.5-0.282) = $399082.

The second part of your question sounds like a homework problem. I'll help you with it if you can make some progress on your own, i.e., at least setting it up. Please send a follow-up and let me know.  

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Randy Patton


Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.


26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

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