Bricktan Inc. makes three products, basic, classic, and deluxe. The maximum Bricktan can sell is 721,000 units of basic, 468,000 units of classic, and 180,000 units of deluxe. Bricktan has limited production capacity of 114,000 hours. It can produce 10 units of basic, 8 units of classic, and 4 units of deluxe per hour. Contribution margin per unit is $15 for the basic, $25 for the classic, and $55 for the deluxe. What is the most profitable sales mix for Bricktan Inc.

When a business is faced with a problem of shortage of a resource which can be used to produced more than one product type, to maximize the use of the resource , the business should allocate the scare resource for production purpose in such a way that it maximizes the contribution per unit of the scare resource.

The labour hours required per unit of scarce resource=

Basic = 1/10 hr= 0.10

Classic =1/8 hr = 0.13

Deluxe= 1/4 hr = 0.25

Basic Classic Deluxe

Contribution per unit 15 25 55

Hour per unit 0.10 0.13 0.25

Contribution per hour 150 200 220

Product Unit Hours used

Deluxe 180,000 180000× 0.25 45,000

Classic 468,000 468,00× 0.13 58,500

Basic 365,000** 365,000×0.10 36,500*

Total hours 140,000

* = 140,000 - 45,000-58500= 36,500 hours

** = 36,500 hours/0.1 hour = 365,000 units

Units to be produced = 36,500/0.10= 365,000 units

Profitable sales mix :

Deluxe - 180,000 units,

Classic - 58,500 units,

Basic- 365,000 units