Texas-Q Company produces and sells barbeque grills. Texas-Q sells three models: a small portable gas grill, a larger stationary gas grill, and the specialty smoker. In the coming year, Texas-Q expects to sell 20,000 portable grills, 50,000 stationary grills, and 5,000 smokers. Information on the three models is as follows:
Portable Stationary Smokers
Price $90 $200 $250
Variable cost per unit 45 130 140
Total fixed cost is $2,128,500.
Required:
1. What is the sales mix of portable grills to stationary grills to smokers?
2. Compute the break-even quantity of each product.

The sales mix is the proportion of sales in units that each product holds in the in relation to the total overall sales in units of all products. The sales mix is calculated as follows,

Sales mix proportion of Product A = Sales in units Product A/Total number of sales in units of all products

The total number of sales in units of all products is,

Total sales in units = 20000 + 50000 + 5000 = 75000 units

Sales mix

Portable grills = 20000/75000 = 4/15 or 26.67%

Stationary grills = 50000/75000 = 2/3 or 66.67%

Smokers = 5000/75000 = 1/15 or 6.67%

2.

We will compute the overall break even point in units in then divide it according to the sales mix to calculate the break even in units of each product.

To calculate the overall break even in units, we need to determine the weighted average contribution per unit.

Weighted average contribution per unit = 4/15 * (90 - 45) + 2/3 * (200 - 130) + 1/15 * (250 - 140)

Weighted average contribution per unit = 66

Break even in units

Overall = 2128500 / 66 = 32250 units

Portable = 32250 * 4/15 = 8600

Stationary = 32250 * 2/3 = 21500

Smokers = 32250 * 1/15 = 2150