Free Quote; Mathematics

One Earth

You work for OneEarth, an environmental consulting company that specializes in building condition assessments, contaminated site remediation, and energy audits. Founded by an environmentally concerned citizen in 2010, OneEarth has emerged as the highest-quality and most comprehensive environmental services company in the region.

Southern New Hampshire University (SNHU), a private nonprofit university located in Manchester, New Hampshire, in the United States, is dedicated to reducing its carbon footprint. SNHU has approached OneEarth for its assistance and expertise in achieving this goal. Knowing of your desires to diversify your experience and professional portfolio, your manager, Claire DeAir, has consented for you to join the team working with SNHU. You’re responsible for creating a technical report based on an analysis of the data the onsite team has collected over the last few weeks to determine the cost-effectiveness of SNHU adopting solar energy.


You’ve been asked to recommend whether or not SNHU should install solar energy panels on one of its buildings in Manchester, New Hampshire, to reduce the university’s carbon footprint. Using the data in the SNHU Site Data document in the Supporting Materials section, you will conduct a series of calculations. With those calculations, you will create a technical report for SNHU that explains whether the university should invest in solar energy by purchasing the system or by leasing. Your technical report should include the following calculations and determinations:

  • A calculation of the total electricity output of a solar panel system in kilowatts hours (kWh)
    Use the following steps as a guide to making this calculation:
    • How many panels fit on the roof, assuming the building is rectangular? (To make this determination, determine the number of panels that can fit along one side, and the number of rows of panels that can fit along the opposite side. Round down to the nearest whole number of panels in each direction and multiply to obtain the required number of panels.)
      • What are the dimensions of the building’s roof in meters?
      • What are the dimensions of each solar panel in centimeters? (To convert from inches to centimeters, multiply the dimensions in inches by 2.54 and do not round until the last step of the calculation.) Find the number of meters for each dimension.
      • How many panels will fit on the roof in each direction? Round down to the nearest panel. When calculating the number of panels, be sure that when you change from length to width on the roof, you also change from length to width on the panels.
      • Find the area of the panels in meters to make sure that the area of the panels is less than the area of the roof.
    • What is the total amount of electricity that could be produced by adopting a solar panel system that covers the entire roof based on the average monthly sunlight? (1kW = 1000W, and 1 hour of sunlight produces 400 watts per panel)
      • How many kW per hour of sunlight could be produced per solar panel? Per entire system (based on how many panels could fit on the roof)?
      • How many hours of sunlight are expected on average per month? Calculate the average hours based on the monthly data provided. Round down to the nearest tenth of an hour.
      • What is the likely average amount of kWh produced per panel based on the average amount of sunlight per month? Per year? Round to the nearest hundredth kWh.
      • What is the total amount of kWh that is produced by the entire solar panel system per month based on the average monthly sunlight? Per year?
  • A calculation of the difference between the current electricity usage of the building and the electricity generated by a solar panel system in kilowatt hours and in dollars
    Use the following steps as a guide to making this calculation:
    • How much electricity does the building use on average annually?
    • What is the estimated total amount of kWh produced by the entire solar panel system on this building per year, based on the average monthly sunlight for the area?
    • Based on the average cost of electricity in the area, about how much is the annual electricity cost for the SNHU building?
      • Is the amount of electricity generated by the solar array sufficient to cover SNHU’s yearly electricity usage?
      • If not, what is the remaining energy needed in kW? How much would this cost in dollars? In other words, what is the remaining utility bill?
      • If the energy generated is more than the energy needed to run the building, how much additional savings is there for energy that can be channeled to other buildings on campus or sold back to the energy company?
  • A determination of the likelihood of receiving a damaged panel
    SNHU expressed some concerns about receiving damaged solar panels from the manufacturer. You would like to be transparent and address these concerns by illustrating the likelihood of a damaged panel based on the size of the system SNHU would be purchasing.

The manufacturer has reported that since solar panels are complex and evolving technology, 1 out of every 1,000 manufactured solar panels is defective.

    • How many panels fit on the roof?
    • What is the probability or likelihood that SNHU will receive a damaged solar panel, based on the number of panels it would be purchasing?
  • A determination of how long it would take to pay back the cost of buying the system in years
    Use the following steps as a guide to making this calculation—you can assume there will not be any required maintenance during the first 10 years:
    • What would be the upfront cost to purchase and install the solar panel system?
      • How much does each panel cost? How much does the entire system cost?
      • How much does installation cost?
      • What are the government incentives? How does that affect the cost?
      • What is the remaining utility cost, if there is one?
    • How much will your solar panels save SNHU per year?
    • How long would it take to pay back the cost of purchasing the solar panel system in years? (Years = Cost to Purchase and Install Solar Panel System / Savings Per Year) The time in years should take into account all energy savings, not just those for the building on which the solar array is installed.
  • A determination of whether there is a cost savings over 10 years for leasing the solar panel system
    Use the following steps as a guide to making this calculation:
    • What is the total cost without solar for 10 years, in dollars?
    • What is the total cost with solar for 10 years, in dollars?
      • How much does it cost to rent the entire solar panel system?
      • What is the total remaining utility bill for 10 years?
    • What are the 10-year savings? (Cost Without Solar for 10 Years – (Cost of Solar Panel Rental for 10 Years + Remaining Utility Bills for 10 Years) = Total 10-Year Saving)
    • Hint: leasing costs should be a substantial fraction of purchase costs without any government incentives. Costs for leasing are typically listed per panel.
  • A recommendation for whether SNHU should install solar energy panels on its buildings based on your calculations
  • An explanation of whether SNHU should invest in a solar energy system by purchasing it upfront or by leasing it (Base your response on your calculations.)
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