Chapter 7.1, Problem 82E

To determine

To determine the functions based on the given information and hence find the solution of the equations both analytically and graphically.

Answer to Problem 82E

Thesolution of the given linear equations is $x=61.70$

Explanation of Solution

Given information: The given information is:

A pellet stove costs $3650 and produces a heat at a cost of 19.15 per 1 million Btu and a electric furnace stove costs $2780 and produces a heat at a cost of 33.25 per 1 million Btu.

Calculation:

Let $y$ be the total cost and $x$ be the heat in million Btu

(a)   $\text{Pellet}\text{Stove: y}=3650+19.15x$

(b)   $\text{Electric Furnance: y}=2780+33.25x$

(c)  Using graphing utility to sketch the following functions:

  $\text{Pellet}\text{Stove: y}=3650+19.15x$ ; $\text{Electric Furnance: y}=2780+33.25x$

The graph of the functions are:

  

(d) The given equations are:

  $\text{y}=3650+19.15x;\text{y}=2780+33.25x$

  $\Rightarrow 3650+19.15x=2780+33.25x$

  $\Rightarrow 14.10x=870$

  $\Rightarrow x=61.70$

Hence, the solution of the given linear equations is $x=61.70$

(e) From the results, it has been found that at 61.70 million Btu of consumption, both type of the sources have the same cost.