Question

Each morning, Max Smith stocks the drink case at Max’s Beach Hut in Myrtle Beach, South Carolina. The drink case has 120 linear feet of refrigerated drink space. Each linear foot can hold either six 12-ounce cans or three 20-ounce bottles.

Max’s Beach Hut sells three types of cold drinks:

1. Licious-Ade in 12-oz. cans for \(1.40 per can

2. Licious-Ade in 20-oz. bottles for \)1.90 per bottle

3. Pep-Cola in 20-oz. bottles for \(2.20 per bottle

Max’s Beach Hut pays its suppliers:

1. \)0.20 per 12-oz. can of Licious-Ade

2. \(0.35 per 20-oz. bottle of Licious-Ade

3. \)0.55 per 20-oz. bottle of Pep-Cola

Max’s Beach Hut’s monthly fixed costs include:

Hut rental \(355

Refrigerator rental 65

Max’s salary 1,700

Total fixed costs \)2,120

Max’s Beach Hut can sell all the drinks stocked in the display case each morning.

Requirements

1. What is Max’s Beach Hut’s constraining factor? What should Max stock to maximize profits?

2. Suppose Max’s Beach Hut refuses to devote more than 80 linear feet to any individual product. Under this condition, how many linear feet of each drink should Max’s stock? How many units of each product will be available for sale each day?

Short answer

The company should stock Licious-Ade in 12-oz. cans forprofit maximization.

Step-by-step solution

Meaning of Profit Maximization  

Profit maximization refers to aprocess of determining thecosts, inputs, and output levelsby a business entity to attain the highest profits in the short and long-run. Such an approach leads businesses to growth and development.

Identification of constraint and solution to it

According to the given scenario, the constraining factor for the company is the linear feet of shelf space.

To resolve the impact of the constraint, Max Smith should stock the drink, which will provide thehighest contribution margin per linear foot of shelf space.

Computation of contribution margin per linear foot of shelf space

Product mix analysis
Particulars	Licious-Ade in 12-oz. cans ($)	Licious-Ade in 20-oz. bottles ($)	Pep-Cola in 20-oz. bottles ($)
Selling price per unit	1.40	1.90	2.20
Less: Variable cost per unit	(0.20)	(0.35)	(0.55)
Contribution margin per unit (a)	1.20	1.55	1.65
Units per linear foot of shelf space (b)	6	3	3
Contribution margin per linear foot of shelf space (a*b)	$7.20	$4.65	$4.95

Computation of maximum profit

As per the above product mix analysis, the company should stock Licious-Ade in 12-oz. cans because it givesthe highest contribution marginper linear foot of shelf space.

Maximum profit:

$\begin{array}{rcl}\text{Maximum profit}& =& \text{Contribution margin per linear foot}\times \text{Total space}\\ & =& \$7.20\times 120\\ & =& \$864\\ & & \end{array}$

Computation of units to be stocked

Max Smith should stock 80 units of the product that provides the highest contribution margin per linear foot of shelf space and 40 units of the second-highestcontribution marginproduct.

Computation of stock as per shelf space:

Particulars	Units for sale
Licious-Ade in 12-oz. cans (80*6)	480
Licious-Ade in 20-oz. bottles (40*3)	120
Pep-Cola in 20-oz. bottles	0
Total	600