Topics: Linear programming formulation, converting fractional constraints to linear constraints. Difficulty: Medium The Connecticut public utility company EverCore in has identified a 2 hectare (= 20,000 square meters) parcel of land to create a solar farm and is considering two types of solar panels for installation: fixed panels and tracking panels (the latter tilt their orientation to track the sun). Though the two types of panels are of the same size, tracking panels must be installed with more space between rows to allow access for maintenance of the tracking mechanism. Fixed panels require 3.75 sq.m. of area per panel and tracking panels require 4 sq.m. per panel (which means that if only one type of panel is installed, the farm can have up to 5,333 fixed panels or 5,000 tracking panels, but the solar farm can be divided arbitrarily between the two types of panels). Tracking panels generate more solar energy than fixed panels on average, but on a cloudy day, the fixed panel is somewhat more efficient. Solar power generation varies not only with the length of the day, but also with cloud cover and weather conditions like snow accumulation. The annual average and low energy generation from each panel is estimated in the table below. The tracking panels are more expensive than fixed panels, as is their installation cost. The table provides the per panel cost including installation. Annual energy output per panel (kWh) Panel type Fixed Tracking Low Average Cost per panel Area per panel (incl. installation) (sq.m.) 100 95 115 150 3.75 4 $950 $1,100 EverCore has a budget of $5.2 million for the project. Its goal is to maximize the average annual energy generation from the farm, but wants to make sure that the output in a low year will still exceed 500MWh (1MWh = 1,000kWh). (a) Build an LP model to determine how many fixed and tracking panels it should install to maximize the average annual energy generation, subject to the constraints of budget, available land, and the 500MWh requirement in a low year. Write down the mathematical model by carefully defining its decision variables and labelling the objective and constraints. You may write the mathematical formulation either in the space below, or upload an image or PDF in the next question.

Topics: Linear programming formulation, converting fractional constraints to linear constraints. Difficulty: Medium The Connecticut public utility company EverCore in has identified a 2 hectare (= 20,000 square meters) parcel of land to create a solar farm and is considering two types of solar panels for installation: fixed panels and tracking panels (the latter tilt their orientation to track the sun). Though the two types of panels are of the same size, tracking panels must be installed with more space between rows to allow access for maintenance of the tracking mechanism. Fixed panels require 3.75 sq.m. of area per panel and tracking panels require 4 sq.m. per panel (which means that if only one type of panel is installed, the farm can have up to 5,333 fixed panels or 5,000 tracking panels, but the solar farm can be divided arbitrarily between the two types of panels). Tracking panels generate more solar energy than fixed panels on average, but on a cloudy day, the fixed panel is somewhat more efficient. Solar power generation varies not only with the length of the day, but also with cloud cover and weather conditions like snow accumulation. The annual average and low energy generation from each panel is estimated in the table below. The tracking panels are more expensive than fixed panels, as is their installation cost. The table provides the per panel cost including installation. Annual energy output per panel (kWh) Panel type Fixed Tracking Low Average Cost per panel Area per panel (incl. installation) (sq.m.) 100 95 115 150 3.75 4 $950 $1,100 EverCore has a budget of $5.2 million for the project. Its goal is to maximize the average annual energy generation from the farm, but wants to make sure that the output in a low year will still exceed 500MWh (1MWh = 1,000kWh). (a) Build an LP model to determine how many fixed and tracking panels it should install to maximize the average annual energy generation, subject to the constraints of budget, available land, and the 500MWh requirement in a low year. Write down the mathematical model by carefully defining its decision variables and labelling the objective and constraints. You may write the mathematical formulation either in the space below, or upload an image or PDF in the next question.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 13T

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