Question 101695
A small family bakery specializes in baking cheesecakes. The fixed cost of production is $245, the marginal cost per cheesecake is $5, and each cheesecake sells for $12. Assume that the cost function is linear.
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Let x = no. of cheesecakes made and sold
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a. What is the cost function?
The cost function will be the cost to make the cakes plus the fixed cost:
C = 5x + 245
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b. What is the revenue function?
The Revenue is the total amt received from the sale of the cakes:
R = 12x
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c. What is the break-even point?
Break-even point occurs when Cost = Revenue, solve for x,
That will give you the number of cakes that must be sold to break even
R = C
12x = 5x + 245
12x - 5x = 245
7x = 245
x = 245/7
x = 35 cakes need to be sold to break even. (Less they would lose money, more they will make money)
:
:
you can check out solution by substituting 35 for x and see of cost and revenue are equal
Revenue:
 12*35 = $420
and Cost:
5*35  + 245 =
175 + 245 = $420 also
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Did this help you find your way? Any questions?