Chapter 7, Problem 9P

Metters Cabinets, Inc., needs to choose a production method for its new office shelf, the Maxistand. To help accomplish this, the firm has gathered the following production cost data:

Metters Cabinets projects an annual demand of 24,000 units for the Maxistand. The Maxistand will sell for $120 per unit. a) Which process type will maximize the annual profit from producing the Maxistand?

b) What is the value of this annual profit?

Summary Introduction

To determine: The process type that will maximize the annual profit by producing the Maxistand.

Answer to Problem 9P

The process type that will maximize the annual profit by producing the Maxistand is the intermittent process.

Explanation of Solution

Given information:

Process type	Annual fixed cost of plant & equip	Variable costs (Per Unit) ($)
		Labor	Material	Energy
Mass customization	$1,260,000	30	18	12
Intermittent	$1,000,000	24	26	20
Repetitive	$1,625,000	28	15	12
Continuous	$1,960,000	25	15	10

Annual demand = 24,000 units

Maxistand selling price = $120 / unit

Calculation of number of units:

Let ‘x’ be the number of units. The units is calculated by multiplying annual fixed cost with ‘x’ and summing with the total variable cost and equating it with multiplying the Maxistand selling price with ‘x’.

Mass customization:

$\begin{array}{c}1,260,000+\left(\text{30}+\text{18}+\text{12}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,260,000}+\text{60x}=\text{120x}\\ \text{1,260,000}=\text{120x}-\text{60x}\end{array}$

$\begin{array}{c}\text{1,260,000}=\text{60x}\\ \text{x}=\frac{\text{1,260,000}}{\text{60}}\\ \text{x}=\text{21,000}\end{array}$

Intermittent:

$\begin{array}{c}\text{1,000,000}+\left(\text{24}+\text{26}+\text{20}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,000,000}+\text{70x}=\text{120x}\\ \text{1,260,000}=\text{120x}-\text{70x}\end{array}$

$\begin{array}{c}\text{1,000,000}=\text{50x}\\ \text{x}=\frac{\text{1,000,000}}{\text{50}}\\ \text{x}=\text{20,000}\end{array}$

Repetitive:

$\begin{array}{c}\text{1,625,000}+\left(\text{28}+\text{15}+\text{12}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,625,000}+\text{55x}=\text{120x}\\ \text{1,625,000}=\text{120x}-\text{55x}\end{array}$

$\begin{array}{c}\text{1,625,000}=\text{65x}\\ \text{x}=\frac{\text{1,625,000}}{\text{65}}\\ \text{x}=\text{25,000}\end{array}$

Continuous:

$\begin{array}{c}\text{1,960,000}+\left(\text{25}+\text{15}+\text{10}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,960,000}+\text{50x}=\text{120x}\\ \text{1,960,000}=\text{120x}-\text{50x}\end{array}$

$\begin{array}{c}\text{1,960,000}=\text{70x}\\ \text{x}=\frac{\text{1,960,000}}{\text{70}}\\ \text{x}=\text{28,000}\end{array}$

Identifying least cost process at x = 24000 units:

The least cost is calculated by multiplying variable cost with the value of ‘x’ and summing it with the annual fixed cost.

Mass customization:

$\begin{array}{c}\text{Mass}\text{customization}=\text{1,260,000}+\left(\text{30}+\text{18}+\text{12}\right)\text{x}\\ =\text{1,260,000}+\text{60x}\\ =\text{1,260,000}+\left(\text{60}\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,260,000}+\text{1,440,000}\\ =\text{2,700,000}\end{array}$

Intermittent:

$\begin{array}{c}\text{Intermittent}=\text{1,000,000}+\left(24+26+20\right)\text{x}\\ =\text{1,000,000}+7\text{0x}\\ =\text{1,000,000}+\left(\text{70}\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,000,000}+\text{1,680,000}\\ =\text{2,680,000}\end{array}$

Repetitive:

$\begin{array}{c}\text{Repetitive}=\text{1,625,000}+\left(28+15+12\right)\text{x}\\ =\text{1,625,000}+55\text{x}\\ =\text{1,625,000}+\left(55\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,625,000}+\text{1,320,000}\\ =\text{2,945,000}\end{array}$

Continuous:

$\begin{array}{c}\text{Continuous}=\text{1,960,000}+\left(25+15+10\right)\text{x}\\ =\text{1,960,000}+50\text{x}\\ =\text{1,960,000}+\left(\text{50}\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,960,000}+\text{1,200,000}\\ =3\text{,160,000}\end{array}$

The cost is lower for intermittent process ($2,680,000) with the break-even point of 20,000. The intermittent process will increase the annual profit.

Hence, the best process is the intermittent process.

Summary Introduction

To determine: The annual profit by following the intermittent process.

Answer to Problem 9P

The annual profit is $200, 000

Explanation of Solution

Given information:

Process type	Annual fixed cost of plant & equip	Variable costs (Per Unit) ($)
		Labor	Material	Energy
Mass customization	$1,260,000	30	18	12
Intermittent	$1,000,000	24	26	20
Repetitive	$1,625,000	28	15	12
Continuous	$1,960,000	25	15	10

Annual demand = 24,000 units

Maxistand selling price = $120 / unit

Calculation of number of units:

Let ‘x’ be the number of units. The units is calculated by multiplying annual fixed cost with ‘x’ and summing with the total variable cost and equating it with multiplying the Maxistand selling price with ‘x’.

Mass customization:

$\begin{array}{c}1,260,000+\left(\text{30}+\text{18}+\text{12}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,260,000}+\text{60x}=\text{120x}\\ \text{1,260,000}=\text{120x}-\text{60x}\end{array}$

$\begin{array}{c}\text{1,260,000}=\text{60x}\\ \text{x}=\frac{\text{1,260,000}}{\text{60}}\\ \text{x}=\text{21,000}\end{array}$

Intermittent:

$\begin{array}{c}\text{1,000,000}+\left(\text{24}+\text{26}+\text{20}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,000,000}+\text{70x}=\text{120x}\\ \text{1,260,000}=\text{120x}-\text{70x}\end{array}$

$\begin{array}{c}\text{1,000,000}=\text{50x}\\ \text{x}=\frac{\text{1,000,000}}{\text{50}}\\ \text{x}=\text{20,000}\end{array}$

Repetitive:

$\begin{array}{c}\text{1,625,000}+\left(\text{28}+\text{15}+\text{12}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,625,000}+\text{55x}=\text{120x}\\ \text{1,625,000}=\text{120x}-\text{55x}\end{array}$

$\begin{array}{c}\text{1,625,000}=\text{65x}\\ \text{x}=\frac{\text{1,625,000}}{\text{65}}\\ \text{x}=\text{25,000}\end{array}$

Continuous:

$\begin{array}{c}\text{1,960,000}+\left(\text{25}+\text{15}+\text{10}\right)\text{x}=\text{120}\times \text{x}\\ \text{1,960,000}+\text{50x}=\text{120x}\\ \text{1,960,000}=\text{120x}-\text{50x}\end{array}$

$\begin{array}{c}\text{1,960,000}=\text{70x}\\ \text{x}=\frac{\text{1,960,000}}{\text{70}}\\ \text{x}=\text{28,000}\end{array}$

Identifying least cost process at x = 24000 units:

The least cost is calculated by multiplying variable cost with the value of ‘x’ and summing it with the annual fixed cost.

Mass customization:

$\begin{array}{c}\text{Mass}\text{customization}=\text{1,260,000}+\left(\text{30}+\text{18}+\text{12}\right)\text{x}\\ =\text{1,260,000}+\text{60x}\\ =\text{1,260,000}+\left(\text{60}\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,260,000}+\text{1,440,000}\\ =\text{2,700,000}\end{array}$

Intermittent:

$\begin{array}{c}\text{Intermittent}=\text{1,000,000}+\left(24+26+20\right)\text{x}\\ =\text{1,000,000}+7\text{0x}\\ =\text{1,000,000}+\left(\text{70}\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,000,000}+\text{1,680,000}\\ =\text{2,680,000}\end{array}$

Repetitive:

$\begin{array}{c}\text{Repetitive}=\text{1,625,000}+\left(28+15+12\right)\text{x}\\ =\text{1,625,000}+55\text{x}\\ =\text{1,625,000}+\left(55\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,625,000}+\text{1,320,000}\\ =\text{2,945,000}\end{array}$

Continuous:

$\begin{array}{c}\text{Continuous}=\text{1,960,000}+\left(25+15+10\right)\text{x}\\ =\text{1,960,000}+50\text{x}\\ =\text{1,960,000}+\left(\text{50}\times \text{24,000}\right)\end{array}$

$\begin{array}{c}=\text{1,960,000}+\text{1,200,000}\\ =3\text{,160,000}\end{array}$

Calculation of annual profit:

The annual profit is calculated by multiplying the selling price with annual demand and subtracting it from the cost of the intermittent process.

$\begin{array}{c}\text{Profit}=\left(\text{120}\times \text{24,000}\right)-\text{2,680,000}\\ =\text{2,880,000}-\text{2,680,000}\\ =\text{200,000}\end{array}$

The annual profit is $200, 000.