If a private company with break-even operations received a $10 million investment, how would you develop a strategy to spend or invest that money?

It is assumed the company has been operating a level where it's fixed expenses are equal to it contribution  (Revenue less variable cost).  If the company has excess capacity  to produce more units of its product and has enough market for its product, then the company can use this additional funds for additional production.  If there is no additional capacity, they company can plan to expand its capacity, subject to availability of market for its products.

The calculation of break-even analysis may be performed using two formulas. First, the total fixed costs are divided the unit contribution margin. In the example above, assume total company fixed costs are $20,000. With a contribution margin of $40, the break-even point is 500 units ($20,000 divided by $40). Upon the sale of 500 units, all fixed costs will be paid for, and the company will report a net profit or loss of $0.

Alternatively, the break-even point in sales dollars is calculated by dividing total fixed costs by the contribution margin ratio. The contribution margin ratio is the contribution margin per unit divided by the sale price. Using the example above, the contribution margin ratio is 40% ($40 contribution margin per unit divided by $100 sale price per unit). Therefore, the break-even point in sales dollars is $50,000 ($20,000 total fixed costs divided by 40%). This figured may be confirmed as the break-even in units (500) multiplied by the sale price ($100) equals $50,000.