Cullumber, Inc. produces three types of balloons—small, medium, and large—with the following characteristics: Small Medium Large Selling price per unit $6 $8 $10 Variable cost per unit 3 5 6 Contribution margin per unit $3 $3 $4 Machine hours per unit 1 2.4 3 Demand in units 600 1,190 880 The company has only 2,000 machine hours available each month. How many units of each type of balloon should the company make to maximize its total contribution margin? (Round answers to 0 decimal places, e. g. 5,275.)

Small Balloons - 600 units

Medium Balloons - 0 units

Large Balloons - 467 units

Explanation:

To solve this question, the Contribution margin per hour must be ascertained to find out which product is manufactured more efficiently in relation to machine hours.

Small Balloon.

= Contribution margin per unit/ Machine hours per unit

= 3/1

= 3

Medium Balloon.

= Contribution margin per unit/ Machine hours per unit

= 3/2.4

= 1.25

Large Balloon

= Contribution margin per unit/ Machine hours per unit

= 4/3

= 1.33

From the above we can rank the most efficient.

Efficiency Ranking

Small Balloon - 1

Large Balloon - 2

Medium - Balloon 3

As a rule, it is better that a company produces goods it is more efficient at first,

Small Balloons will be produced first and have a demand of 600 units.

With a cost of 1 unit therefore, producing 600 would be,

= 600 * 1

= 600 machine hours.

With Small Balloons taking 600 hours and with a limit of 2,000 hours we are left with,

= 2,000 - 600

= 1,400 hours.

Next in production is Large Balloons at a demand of 880 units with each unit costing $3,

= 880 * 3

= 2,640 machine hours

Seeing as we only have 1,400 machine hours left all these hours will be converted to used for Large Balloons which means the following number of units will be produced,

= 1,400/3

= 466.67

= 467 units.

The Company should produce in the following order to maximise its total contribution margin.

Small Balloons - 600 units

Medium Balloons - 0 units

Large Balloons - 467 units