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Math and Science Solutions for Businesses/Retail Business - How much should I Pay?


During the planning process for starting a gift shop in a local resort town I began to question and consider different compensation plans for the retail clerks. It was fairly standard in the area to pay retail clerks $6.25 an hour. However, as I visited gift shops that were paying these rather low wages I noticed that the clerks simply took orders and did not sell or try to answer any questions for customers. In a visit to a gift shop in Ft. Lauderdale last spring I struck up a conversation with the owner. She was more than willing to share her experiences about retail clerks. In fact, after a lot of trial and error she decided to pay upper-quartile compensation. This consisted of a base wage of $9.50 an hour and a 3 percent commission on all sales. She mentioned that when she went to this type of system her average transaction size increased by 20 percent and that closure went from 28 percent to 40 percent. More importantly, she found that her bottom line profit rose by 32 percent. In short, by paying more for retail clerks she increased employee productivity and the profits of her store.
For the gift shop that I am planning I initially estimated that traffic would be 30,000 visitors annually and that closure would be 24 percent. I estimated my average transaction size at $32. My gross margin percent would be 60 percent and fixed operating expenses would be $60,000 annually. Variable operating expenses would be 20 percent of sales. Under this plan I would pay two full-time clerks $6.25 an hour and I would fill-in when things got busy.
My new plan, which I want to evaluate, calls for paying the clerks $9 per hour plus 4 percent commission on all sales. Thus, my fixed operating expenses would go up by $3,000 and variable operating expenses would rise to 24 percent of sales. I believe that closure would rise to 32 percent and average transaction size would rise to $36.

Based on the impact each compensation strategy has on the net profit of the business, which one should I pursue? Why? Please tell me which would be best based on the calculations you get from what I noted. Thanks!

Based on your numbers, the new plan should be more profitable. The calculations are:

Initial Plan:

Revenue = (number of visitors)(fraction closure)($ per transaction) = (30000)(0.24)($32) = (7200)($32) = $230,400.

Costs = (fixed) + (variable) + (cost of goods)

fixed = $60,000
variable = 20% of sales = (0.2)(230,400) = $46,080
cost of goods (COG) = (revenue)(1 - gross margin) = $230,400(1-0.6) = $92,160

Total costs = $60,000 + $46,080 + $92,160 = $198,240

Profit = Revenue - Costs = $230,400 - $198,240 = $31,760

Note that, for future reference, the cost per purchase = (COG)/(# of purchases) = ($92,160)/(7200) = $12.8/purchase

New Plan:

Revenue = (30000 visitors)(0.32 closure)($36/ sale) = $345,600

fixed = $63,000
variable = ($345,600)(0.24) = $82,944  <- note that the 4% sales commission is included here
COG = (30000 visitors)(0.32 closure)($12.8/purchase) = $122,880

Total costs = $63,000 + $82,944 + $122,880 = $268,824

Profit = $345,600 - $268,824 = $76,776.

The new plan benefits from both the higher closure rate and size of transaction: to compare
Initial: (0.24)($32) = $7.68 per visitor
New: (32)($36) = $11.52 per visitor.

Hope this helps. Was this a homework problem?


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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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