3. Assuming the same sales mix, at what total sales level would Pure Water be indifferent between using the old equipment and buying the new production equipment

The question is not complete. I want to assume the correct question is this:

Crystal Clear Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcher cume filter that only purifies water meant for drinking.  The unit that attaches to the faucet is sold for $90 and has variable costs of $25. The pitcher-cume-filter sells for $110 and has variable costs of $20. Crystal Clear sells two faucet models for every three pitchers sold. Fixed costs equal $1,200,000.

Assuming the same sales mix, at what total sales level would Crystal Clear be indifferent between using the old equipment and buying the new production equipment? If total sales are expected to be 24,000 units, should Crystal Clear buy the new production equipment?

Explanation:

Let b be the total sales volume at which the company's indifference is based

Let the average contribution in the old system be $80

The profit will be 80b - 1200000

Let the average contribution in the new syste, be $88

The profit will be 88b - 1408000

Now let us equate the two average contributions to get:

80b - 1200000 = 88b - 1408000

Let us find b,

88b - 80b -1408000 = -1200000

8b = -1200000 + 1408000

8b = 208000

b = 208000 / 8 = 26000 units

If total sales are expected to be 24,000 units, and the total sales volume at which the company's indifference is based 26,000 units, therefore Crystal Clear should not buy the new production equipment.

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