Chapter 17, Problem 35P

To determine

(a)

The cost to produce each unit.

Answer to Problem 35P

The total cost per unit is, $\$154.95$.

Explanation of Solution

Given:

Production is, $5000$.

The number of run required are $1500$ machines hours, three set ups of the mixing equipment, and $100$ hours of final inspection time.

Cost per machine hour is, $\$50$.

Cost per set-ups is, $\$3000$.

Cost per inspection hour is, $\$20$.

The material and labor cost per sundial is, $\$95$.

Calculation:

Indirect expenses are $45\%$ of material and labor cost.

Calculate the indirect expenses.

$\begin{array}{c}\text{Indirect}\text{expense}=\$95\times 0.45\\ =\$42.75\end{array}$

Calculate the material and labor cost.

$\text{Material and labor cost}=\text{Production}\left(\begin{array}{l}\text{Direct}\text{Material and labor cost}+\\ \text{indirect expenses}\end{array}\right)$

Substitute $5000$ for production, $\$95$ for direct material cost, $\$42.75$ for indirect expenses.

$\begin{array}{c}\text{Material and labor cost}=5000\left(\$95+\$42.75\right)\\ =\$688750\end{array}$

Calculate the machine cost.

$\text{Machine}\text{cost}=\text{Machine}\text{hour}\times \text{Cost per machine hour}$         ...... (I)

Substitute $1500$ for machine hour, and $\$50$ for cost per machine hour in Equation (I).

$\begin{array}{c}\text{Machine}\text{cost}=1500\times \text{\$50}\\ \text{=\$7500}\end{array}$

Calculate the total set-ups cost.

$\text{Set-ups}\text{cost}=\text{Number}\text{of}\text{set-ups}\times \text{Cost per set-ups}$         ...... (II)

Substitute $3$ for number of set-ups, and $\$3000$ for cost per set-ups in Equation (II).

$\begin{array}{c}\text{Set-ups}\text{cost}=\text{3}\times \$3000\\ =\$9000\end{array}$

Calculate the inspection cost.

$\text{Inspection}\text{cost}=\text{Cost per inspection hour}\times \text{Total}\text{inspection}\text{hour}$         ...... (III)

Substitute $\$20$ for cost per inspection hour, and $100$ for total inspection hour in Equation (III).

$\begin{array}{c}\text{Inspection}\text{cost}=\$20\times 100\\ =\$2000\end{array}$

Calculate the total cost.

$\text{Total}\text{cost}=\left[\begin{array}{l}\text{material and labor cost}+\text{machine cost}+\\ \text{total set-ups cost}+\text{inspection cost}\end{array}\right]$         ...... (IV)

Substitute $\$688750$ for material and labor cost, $\text{\$7500}$ for machine cost, $\$9000$ for set-ups cost, and $\$2000$ for Inspection cost in Equation (IV).

$\begin{array}{c}\text{Total}\text{cost}=\$688750+\text{\$7500}+\$9000+\$2000\\ =\$774750\end{array}$

Calculate the cost per unit.

$\text{Cost}\text{per}\text{unit}=\frac{\text{Total}\text{cost}}{\text{Number}\text{of}\text{units}}$         ...... (V)

Substitute $\$774750$ for total cost, and $5000$ for number of units in Equation (V).

$\begin{array}{c}\text{Total cost per unit}=\frac{\$774750}{\$5000}\\ =\$154.95\end{array}$.

Conclusion:

Therefore, the total cost per unit is, $\$154.95$.

To determine

(b)

The unit sales price.

Answer to Problem 35P

The unit sales price is, $\$182.29$.

Explanation of Solution

Given:

The profit percentage is $15\%$.

Calculation:

Calculate the unit sale price.

$\begin{array}{c}\text{Unit sales price}=\frac{\$154.95}{0.85}\\ =\$182.29\end{array}$.

Conclusion:

Therefore, the unit sales price is, $\$182.29$.

To determine

(c)

The total annual profit for the product.

Answer to Problem 35P

The total annual profit for the product is, $\$820200$.

Explanation of Solution

Given:

The number of runs are, $6$.

Calculation:

Calculate the profit per unit.

$\text{Profit per unit}=\text{Sales}\text{price}-\text{Cost}\text{per}\text{unit}$         ...... (VI)

Substitute $\$182.29$ for sales price, and $\$154.95$ for cost per unit in Equation (VI).

$\begin{array}{c}\text{Profit per unit}=\$182.29-\$154.95\\ =\$27.34\end{array}$

Calculate the total production in six runs.

$\begin{array}{c}\text{Total production in six runs}=\$5000\times 6\\ =30000\end{array}$

Calculate the total profit.

$\text{The total profit=Total production in six runs×profit per unit}$         ...... (VII)

Substitute $30000$ for total production in six run, and $\$27.34$ for profit per unit in Equation (VII).

$\begin{array}{c}\text{The total profit}=30000\times \$27.34\\ =\$820200\end{array}$.

Conclusion:

Therefore, the total annual profit for the product is, $\$820200$.