Chapter 10, Problem 10P

1.

To determine

Calculate the number of cans of each kind of nut sold.

Explanation of Solution

Calculate the number of cans of each kind of nut sold as follows:

Assume, x is cans of cashews sold, hence, walnuts is 2x and almonds is 0.5 x.

$\begin{array}{c}\text{10,000=x+2x+0}\text{.5x}\\ \text{10,000 = 3}\text{.5x}\\ \text{x=2,857}\end{array}$

Substitute the value of x,

$\begin{array}{l}\text{Almonds =0}\text{.5x}\\ \text{Almonds =0}\text{.5×2,857}\\ \text{Almonds =1,429}\end{array}$

$\begin{array}{l}\text{Walnuts =2x}\\ \text{Walnuts =2×2,857}\\ \text{Walnuts =5,714}\end{array}$

2.

To determine

Calcualte the sales mix percentage.

Explanation of Solution

Calcualte the sales mix percentage as follows:

Product	Sales unit	Sales mix percentage $\left(\frac{\text{Product}}{\text{Total}}\times 100\right)$
Almonds	1,429	14.29%
Cashews	2,857	28.57%
Walnuts	5,741	57.14%
Total	10,027	100.00%

Table (1)

3.

To determine

Calcualte the weighted average contribution margin per unit.

Explanation of Solution

Calcualte the weighted average contribution margin per unit as follows:

$\begin{array}{c}\begin{array}{l}\text{Weighted average }\\ \text{contribution }\\ \text{marign per unit}\end{array}\}\text{ =}\frac{\left[\begin{array}{l}\left(\text{Almond unit contribution}\times \text{Almonds sold}\right)+\\ \left(\text{Cashews unit contribution}\times \text{Cashews sold}\right)+\\ \left(\text{Walnuts unit contribution}\times \text{Walnuts sold}\right)\end{array}\right]}{\left(\text{Almonds sold+Cashews sold+Walnuts sold}\right)}\\ \text{=}\frac{\left[\begin{array}{l}\left[\left(\$8-\$4\right)\times 1,429\right]+\\ \left[\left(\$10-\$5\right)\times 2,857\right]+\\ \left[\left(\$6-\$4\right)\times 5,714\right]\end{array}\right]}{\left(1,429+2,857+5,714\right)}\\ \text{=}\frac{\$31,429}{10,000}\\ =\$3.143\end{array}$

4.

To determine

Calcualte the break-even sales volume.

Explanation of Solution

Calcualte the break-even sales volume G as follows:

$\begin{array}{c}\begin{array}{l}\text{Break even sales }\\ \text{volume in units}\end{array}\}\text{ = }\frac{\text{Total fixed costs}}{\text{Weighted average contirbution per unit}}\\ =\frac{\$40,000}{\$3.143}\\ =12,727\text{ units}\end{array}$

5.

To determine

Calculate the unit sales of almonds, cashews and walnuts at the break-even point.

Explanation of Solution

Calculate the unit sales of almonds, cashews and walnuts at the break-even point as follows:

$\begin{array}{c}\begin{array}{l}\text{Units sales }\\ \text{of almonds}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Sales mix percentage }\times \\ \text{Break even sales}\end{array}\right)\\ =14.29\%\times 12,727\\ =1,819\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Units sales }\\ \text{of Cashews}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Sales mix percentage }\times \\ \text{Break even sales}\end{array}\right)\\ =28.57\%\times 12,727\\ =3,636\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Units sales }\\ \text{of walnuts}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Sales mix percentage }\times \\ \text{Break even sales}\end{array}\right)\\ =57.14\%\times 12,727\\ =7,272\end{array}$

6.

To determine

Calcualte the break-even sales in dollars for each product.

Explanation of Solution

Calcualte the break-even sales in dollars as follows:

$\begin{array}{c}\begin{array}{l}\text{Break-even dollars }\\ \text{sales in almonds}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Break even units sales}\times \\ \text{Unit sales price}\end{array}\right)\\ =1,819\times \$8\\ =\$14,552\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Break-even dollars }\\ \text{sales in cashews}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Break even units sales}\times \\ \text{Unit sales price}\end{array}\right)\\ =3,636\times \$10\\ =\$36,360\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Break-even dollars }\\ \text{sales in walnuts}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Break even units sales}\times \\ \text{Unit sales price}\end{array}\right)\\ =7,272\times \$6\\ =\$43,632\end{array}$