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Find the break - even points for company X, which sells all it produces, if the variable cost per unit is $3, fixed costs are $2 and YT R = 5√q, where q is the number of thousands of units of output produced.

User Scr
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1 Answer

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Given:

The variable cost per unit is $3, fixed costs are $2.

The revenue function is:


Y_(TR)=5√(q)

where q is the number of thousands of units of output produced.

To find:

The break - even points for company X.

Solution:

The variable cost per unit is $3, fixed costs are $2.

So, the cost function is:

Total cost = Fixed cost + Variable cost × Quantity


Y_(TC)=2+3q

The revenue function is:


Y_(TR)=5√(q)

At break - even points the profit is zero. It means the cost and revenue are equal.


Y_(TC)=Y_(TR)


2+3q=5√(q)

Squaring both sides, we get


(2+3q)^2=(5√(q))^2


2^2+2(2)(3q)+(3q)^2=25q


4+12q+9q^2-25q=0


4-13q+9q^2=0

Splitting the middle term, we get


4-4q-9q+9q^2=0


4(1-q)-9q(1+q)=0


(4-9q)(1-q)=0

Using zero product property, we get


4-9q=0 and
1-q=0


q=(4)/(9) and
q=1


q\approx 0.444 and
q=1

Therefore, the break even points are 0.444 and 1.

User Broke
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