Question

Kelly Wayne is in the dessert making business. She produces two special “dessert boxes”: (1) Berry Blast and (2) Chocolate Lover. Her operating expenses total $2,000 per week. Kelly is supported by three staff members, who are each responsible for different parts of the dessert box production process.

Herman is responsible for ingredient mixing

Samuel is in charge of decorating the desserts; and

Hazel is the hardest worker of the three. She packages the desserts with great care.

The working capacities of these three workers are as follows:

Activity (Person Assigned)	Estimated minutes per week
Mixing (Herman)	2,400
Decorating (Samuel)	2,400
Packaging (Hazel)	2,400

Other relevant information for the two products appear below:

	Berry Blast	Chocolate Lover
Price per box	$13.00	$11.00
Direct Materials	$3.00	$2.00
Demand per week	500 boxes	400 boxes

Required time required in each activity per box (in minutes) is presented below:

	Berry Blast	Chocolate Lover
Mixing	2	2
Decorating	2	3
Packaging	4	3

Required:

(a) Identify the binding constraint of Kelly Wayne’s business. Show all working.

(b) Based on the constraint you identified, what is the production mix that would maximise profit under current production conditions? Show all workings.

(c) Identify two actions will could be undertaken to ‘elevate’ the constrain you identified in part (a). Explain how the actions you identify will elevate the current constraint.

Answer 1

1. Mixing Hours Required per Week on the basis of Demand: 500*2+400*2 = 1800

Decorating Hours Required per Week on the basis of Demand: 500*2+400*3 = 2200

Packaging Hours Required per Week on the basis of Demand: 500*4+400*3 = 3200

Hours Available for each activity on the basis of current distribution of work: 2400 hours per week

• Packaging Hours becomes the binding constraint of Kelly Wayne’s business.

2.Statement of Contribution per Limiting Factor i.e. Packaging Hours

	Berry Blast	Chocolate Lover
Contribution per Box	10	9
Packaging Hours	4	3
Contribution per Packaging Hour	2.5	3
Rank	2	1

Statement of Optimim Product Mix (per Week) :

Product	Units (Boxes)	Packaging Hours Per Unit	Total Packaging Hours
Berry Blast	300	4	1200
Chocolate Lover	400	3	1200
			2400

Available hours will first be utilised for Chocolate Lover because it is providing higher contribution per limiting factor i.e. Packaging Hours.

3.Action 1: We have spare unutilised hours available for Herman and Samuel, those can be used in packaging the remaining 200 boxes. Both of them can be trained and then we will be able to meet the remaining demand of 200 boxes. Spare Hours Available = 600+200 = 800, which is exactly equal to the time required to package the remaining boxes.

Action 2: Another possible action could be to increase the Hazel’s available time by 800 minutes. If not possible, hire anybody else but that would cost Kelly Wayne some incremental cost which can be avoided using the first recommended action.