Question

Blossom, Inc., is a small company that manufactures three versions of patio tables. Unit information for its products follows:

		Table A		Table B		Table C
Sales price		$	47	$	51	$	65
Direct materials			9		10		11
Direct labor			2		4		8
Variable manufacturing overhead			3		3		3
Fixed manufacturing overhead			6		6		6
Required number of labor hours			0.50		0.50		1.00
Required number of machine hours			4.00		2.50		2.00

Blossom has determined that it can sell a limited number of each table in the upcoming year. Expected demand for each model follows:

Table A	50,000	units
Table B	30,000	units
Table C	20,000	units

Required:
1. Suppose that direct labor hours has been identified as the bottleneck resource. Determine how Blossom should prioritize production by rank ordering the products from 1 to 3.
2. If Blossom has only 45,000 direct labor hours available, calculate the number of units of each table that Blossom should produce to maximize its profit.
3. Suppose that the number of machine hours has been identified as the most constrained resource. Determine how Blossom should prioritize production by rank ordering the products from 1 to 3.
4. If Blossom has only 239,000 machine hours available, calculate the number of units of each table that Blossom should produce to maximize its profit.

Answer 1

1) If direct labor hours are in constrained, contribution margin per direct labor hour is required to be calculated which is shown as follows:- (Amounts in $)

		Table A		Table B		Table C
Sales price (A)			47		51		65
Less: Variable Costs
Direct materials			9		10		11
Direct labor			2		4		8
Variable manufacturing overhead			3		3		3
Total Variable Costs (B)			14		17		22
Contribution Margin per unit (C = A/B)			33		34		43
Required number of labor hours (D)			0.50		0.50		1.00
Contribution Margin per labor hour (C/D)			66		68		43
Ranking			2		1		3

On the basis of contribution margin per labor hour, ranking is given to all the three tables. The rank 1 is given to highest contribution per labor hour and so on.

2) Calculation of no. of units to be produced   

Product based on ranking	Expected demand	Labor hour required per unit	Units to be produced	Labor hours used	Remaining Labor hours
Table B	30,000 units	0.50 hr	30,000 units	15,000 hrs (30,000*0.50)	30,000 hrs (45,000-15,000)
Table A	50,000 units	0.50 hr	50,000 units	25,000 hrs (50,000*0.50)	5,000 hrs (30,000-25,000)
Table C	20,000 units	1 hr	5,000 units	5,000 hrs (remaining)	0

Therefore the company should produce 30,000 units of Table B, 50,000 units of Table A and 5,000 units of Table C to maximize profit.

3) If machine hours are in constrained, contribution margin per machine hour is required to be calculated which is shown as follows:- (Amounts in $)

		Table A		Table B		Table C
Sales price (A)			47		51		65
Less: Variable Costs
Direct materials			9		10		11
Direct labor			2		4		8
Variable manufacturing overhead			3		3		3
Total Variable Costs (B)			14		17		22
Contribution Margin per unit (C = A/B)			33		34		43
Required number of machine hours (D)			4.00		2.50		2.00
Contribution Margin per machine hour (C/D)			8.25		13.60		21.5
Ranking			3		2		1

On the basis of contribution margin per machine hour, ranking is given to all the three tables. The rank 1 is given to highest contribution per machine hour and so on.

4) Calculation of no. of units to be produced   

Product based on ranking	Expected demand	Machine hrs required per unit	Units to be produced	Labor hours used	Remaining Labor hours
Table C	20,000 units	4.00 hrs	20,000 units	80,000 hrs (20,000*4.00)	159,000 hrs (239,000-80,000)
Table B	30,000 units	2.50 hrs	30,000 units	75,000 hrs (30,000*2.50)	84,000 hrs (159,000-75,000)
Table A	50,000 units	2.00 hrs	42,000 units (84,000/2 hrs)	84,000 hrs (remaining)	0

Therefore the company should produce 20,000 units of Table C, 30,000 units of Table B and 42,000 units of Table A to maximize profit.