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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
x = 32000/500 = 64. So x= 24 is the break even value and if you manufacture more you are in profit.
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
80 units must be manufactured and sold to break even.
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