Boston’s Dairy has just opened its main yogurt factory in upstate Massachusetts. This main factory can produce 3,500 boxes of yogurt monthly (each box contains twelve 6-oz cups). Due to overwhelming demand for the company’s product, Boston’s Dairy has signed a contract to rent a new factory, which can produce up to 8,000 boxes per month. The monthly total fixed costs are $40,000 in the main factory and $16,000 in the new factory. The variable production cost of yogurt is $4.50 per box in the main factory. The variable production cost in the new factory is $6.0 per box as materials have to be redistributed from the main factory. The average selling price is $15, and the variable selling expense is $1 per box, which is the same for all factories. In addition, Boston’s Dairy plans to pay its sales force $0.80 per box as added bonus for every box sold above the break-even point. How many boxes does the company have to produce and sell in order to earn a net operating income of $10,000 per month (round all decimal up to one box)

7,733 units

Explanation:

Breakeven point is one where revenue equals the cost.

In the main Factory:

Fixed cost = $40,000

Variable cost = $19,250  [($4.5 + $1.0) * 3,500 boxes]

Total cost = $59,250 [$40,000 + $19,250]

Revenue = $52,500 [3,500 * $15]

Net profit or loss : $52,500 - $59,250 = - 6,750 Loss

In the new Factory:

The break even point will be achieved when the loss of $6,750 in the main factory is covered by the new factory.

Fixed cost : $16,000

Variable cost : $6.0 + $1.0 = $7

Selling price = $15

16,000 + 6,750 + 7x = 15x

solving for x we get:

x = 2,844.

In the new factory 2,844 units needs to be produced in excess to achieve the breakeven point.

Total units required to produce 3,500 + 2,844 = 6,344.

If the company adds bonus of $0.80 for its sales force on each box sold above the breakeven then the cost will be increased.

Contribution Margin : 15 - [ 6 + 1 + 0.80 ] = $7.20

Box required to sell to produce net operating income of $10,000

10,000 / 7.20 = 1,389 units

Total units 7,733 [6,344 + 1,389]

the correct answer for apex is “ doubling a recipe and figuring out how many cups of paint to use are both examples of using math skills”.