Question

Hy work Santana Rey has found that Business Solutions's line of computer desks and chairs has become very popular, and she is finding it hard to keep up with demand. She knows that she cannot fill all of her orders for both items, so she decides she must determine the optimal sales mix given the resources she has available. Information about the desks and chairs follows. Selling price per unit Variable costs per unit Contribution margin per unit Direct labor hours per unit Expected demand for next quarter Desks $1,356.50 530.00 $ 826.50 6 hours 168 desks Chairs $530.00 300.00 $230.00 5 hours 47 chairs Santana has determined that she only has 1168 direct labor hours available for the next quarter and wants to optimize her contribution margin given the limited number of direct labor hours available. Required: Determine the optimal sales mix and the contribution margin the business will earn at that sales mix. (Round per unit amounts to 2 decimal places.)

Answer 1

		Desks	Chairs
a	Contribution margin per unit	826.50	230.00
b	Direct Labour hour per unit	6.00	5.00
c (a/b)	Contribution per direct labour hour	137.75	38.33
	Preference for production	1.00	2.00
	Max. no. of units to be sold	168.00	47.00
	Direct Labour hour per unit	6.00	5.00
	Hours required to produce max. units	1,008.00	235.00
d	No. of desks that can be produced in available labour hour		194.67
e	Max demand for desks		168.00
f	Hence, no. of desks to be produced (Lower of d &e)		168.00
g	Available labour hour		1,168.00
h	Labour hour for 168 desks		1,008.00
I (g-h)	Balance no. of hours available for chairs		160.00
j (i-b)	No. of chairs that can be produced in the available hours		32.00
	Optimal Sales Mix:
		Desks	Chairs
	Hours dedicated for each product	1,008.00	160.00	1,168.00
	Units produced for most profitable sales mix (f&j)	168.00	32.00
	Contribution margin per unit	826.50	230.00
	Total contribution margin	138,852.00	7,360.00