Chapter SH, Problem 6.1MPS

(a)

To determine

To find: The equation for cost of supply and the income.

Answer to Problem 6.1MPS

The equation for the cost of supply is $y=0.50x+20$ , and equation for the income is $y=x$ .

Explanation of Solution

Given information:

The given time cost of the candy mold is $\$20$ , and cost of ingredients for each lollipop is $\$0.50$ , and selling price of $1$ candy is $\$1.00$ .

Calculation:

Calculate the equation.

An equation for the cost of supply $y$ for the number of lollipops sold $x$ and an equation for the income $y$ for the number of lollipops sold $x$ .

The equation for the cost of supply is,

  $y=0.50x+20$

And the equation for the income $y$ is,

  $\begin{array}{l}y=1\times x\\ y=x\end{array}$

Therefore, the equation for the cost of supply is $y=0.50x+20$ , and equation for the income is $y=x$ .

(b)

To determine

To graph: For the each equation.

Explanation of Solution

Given information:

The given equations are $y=0.50x+20$ , $y=x$ .

Graph:

The graph for the equations $y=0.50x+20$ , and $y=x$ is shown below.

  

Graph $\left(1\right)$

Interpretation: The graph for the equations $y=0.50x+20$ , and $y=x$ is shown in figure $\left(1\right)$ .

(c)

To determine

To find: The numbers of lollipops to sell before they begin to make profit.

Answer to Problem 6.1MPS

The number of lollipops to be sold is $40$ .

Explanation of Solution

Given information:

The given time cost of the candy mold is $\$20$ , and cost of ingredients for each lollipop is $\$0.50$ , and selling price of $1$ candy is $\$1.00$ .

Calculation:

Calculate the numbers of lollipops.

  $y=0.50x+20$

  $y=x$

Put $y=x$ in $y=0.50x+20$ .

  $\begin{array}{c}y=0.50x+20\\ x-0.50x=20\\ x=\frac{20}{0.50}\\ x=40\end{array}$

Therefore, the number of lollipops to be sold is $40$ .