Chapter 7.1, Problem 82E

(a)

To determine

To evaluate: The total cost $y$ of buying the pellet stove and producing $x$ million Btu of heat.

Answer to Problem 82E

Therefore, the function for total cost $y=3660+x\times 20.72$ .

Explanation of Solution

Given information: Pellet stove $3660 and produces heat at a cost of $20.72 per 1 million Btu.

Calculation: The total cost of buying pellet stove,

  $\begin{array}{l}\text{Let }y\text{ is the total cost and }x\text{ is per million Btu}\text{.}\\ y=3660+x\times 20.72\end{array}$

Therefore, the function for total cost $y=3660+x\times 20.72$ .

(b)

To determine

To evaluate: The total cost $y$ of buying the electric furnace and producing $x$ million Btu of heat.

Answer to Problem 82E

Therefore, the function for total cost $y=2690+x\times 40.26$ .

Explanation of Solution

Given information: Electricfurnace $2690 and produces heat at a cost of $40.26 per 1 million Btu.

Calculation: The total cost of buying pellet stove,

  $\begin{array}{l}\text{Let }y\text{ is the total cost and }x\text{ is per million Btu}\text{.}\\ y=2690+x\times 40.26\end{array}$

Therefore, the function for total cost $y=2690+x\times 40.26$ .

(c)

To determine

To graph: The two cost functions and solve the system of equations.

Answer to Problem 82E

Therefore, the solution of system $x=49.64\text{ and }y=4688.54$ .

Explanation of Solution

Given information: Pellet stove $3660 and produces heat at a cost of $20.72 per 1 million Btu and Electric furnace $2690 and produces heat at a cost of $40.26 per 1 million Btu.

Calculation: The total cost of buying pellet stove and electric furnace,

  $\begin{array}{l}\text{Let }y\text{ is the total cost and }x\text{ is per million Btu}\text{.}\\ y=3660+x\times 20.72\\ y=2690+x\times 40.26\end{array}$

  

  $\begin{array}{l}y=3660+20.72x\mathrm{...}\left(1\right)\\ y=2690+40.26x\mathrm{...}\left(2\right)\\ \text{Equating both equation,}\\ \text{3660+20}\text{.72}x=2690+40.26x\\ 3660-2690=40.26x-20.72x\\ 970=19.54x\\ x=49.64\\ \text{Putting value }x\text{ in equation}\left(1\right),\\ y=3660+20.72\times x\\ y=3660+20.72\times 49.64\\ y=4688.54\end{array}$

Therefore, the solution of system $x=49.64\text{ and }y=4688.54$ .

(d)

To determine

To evaluate: The two cost functions and solve the system of equations.

Answer to Problem 82E

Therefore, the solution of system $x=49.64\text{ and }y=4688.54$ .

Explanation of Solution

Given information: Pellet stove $3660 and produces heat at a cost of $20.72 per 1 million Btu and Electric furnace $2690 and produces heat at a cost of $40.26 per 1 million Btu.

Calculation: The total cost of buying pellet stove and electric furnace,

  $\begin{array}{l}\text{Let }y\text{ is the total cost and }x\text{ is per million Btu}\text{.}\\ y=3660+x\times 20.72\\ y=2690+x\times 40.26\end{array}$

  $\begin{array}{l}y=3660+20.72x\mathrm{...}\left(1\right)\\ y=2690+40.26x\mathrm{...}\left(2\right)\\ \text{Equating both equation,}\\ \text{3660+20}\text{.72}x=2690+40.26x\\ 3660-2690=40.26x-20.72x\\ 970=19.54x\\ x=49.64\\ \text{Putting value }x\text{ in equation}\left(1\right),\\ y=3660+20.72\times x\\ y=3660+20.72\times 49.64\\ y=4688.54\end{array}$

Therefore, the solution of system $x=49.64\text{ and }y=4688.54$ .

(e)

To determine

To interpret: The results in the context of the situation.

Answer to Problem 82E

Therefore,

Explanation of Solution

Given information: Pellet stove $3660 and produces heat at a cost of $20.72 per 1 million Btu and Electric furnace $2690 and produces heat at a cost of $40.26 per 1 million Btu.

Calculation: The total cost of buying pellet stove and electric furnace,

  $\begin{array}{l}\text{Let }y\text{ is the total cost and }x\text{ is per million Btu}\text{.}\\ y=3660+x\times 20.72\\ y=2690+x\times 40.26\end{array}$