Y= 32,000 + 1,300x Cost equation

y= 1,700x (mowers) Revenue equation

How many units must be manufactured and sold each day for the company to break even.

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For a break even cost of production is equal to revenue. And if the revenue exceeds, there is profit. If the revenue is below the cost of production, there is loss.

y=1700x = 32000+1300x Or

(1700-1300)x=32000. Or

500x=32000. Or

x = 32000/500 = 64. So x= 24 is the break even value and if you manufacture more you are in profit.

Given:

Cost = Y = 32000 + 1300x

Revenue = y = 1700x

At the break even point:

Cost = Revenue

Substituting the function for cost and revenue in the above equation we get:

32000 + 1300x = 1700x

We solve this equation for x as follows:

1700x - 1300x = 32000

400x = 32000

x = 32000/400 = 80

Answer:

80 units must be manufactured and sold to break even.

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