Question

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. Santana has determined that she only has 1,015 direct labor hours available for the next quarter and wants to optimize her contribution margin given the limited number of direct labor hours available.

Selling price per unit . \(1,125 \)375

Variable costs per unit 500 200

Contribution margin per unit . \( 625 \)175

Direct labor hours per unit . 5 hours 4 hours

Expected demand for next quarter 175 desks 50 chairs

Required

Determine the optimal sales mix and the contribution margin the business will earn at that sales mix.

Short answer

The total contribution margin of the sales mix is $115,500.

Step-by-step solution

Definition of contribution margin

The contribution margin is the difference between the unit portion of selling price and variable cost.

Step 2:Calculation of the correct sales mix

	Desk	Chair
Contribution Margin per Unit	$625	$175
Direct Labor Hours per Unit	5 hours	4 Hours
Contribution per Direct Labor Hour	$125	$43.75
	Desk	Chair
Maximum Numbers of Units Sold	175	50
Hours Required to Produce Maximum Number of Units	875	200
For Most Profitable Sales Mix:
	Desk	Chair	Total
Hours Dedicated to the production of each product	875	140	1,015
Units Produced for the most profitable Sales Mix	175	35
Contribution Margin Per Unit	$625	$175
Total Contribution Margin	$109,375	$6,125	$115,500