Question

Peggy Lane​ Corp., a producer of machine​ tools, wants to move to a larger site. Two alternative locations have been​ identified: Bonham and McKinney. Bonham would have fixed costs of $ 820 comma 000 per year and variable costs of $ 13 comma 000 per standard unit produced. McKinney would have annual fixed costs of $ 960 comma 000 and variable costs of $ 12 comma 000 per standard unit. The finished items sell for $ 29 comma 000 each. ​a) The volume of output at which both the locations have the same profit​ = nothing standard units ​(round your response to the nearest whole​ number).

Answer 1

Answer:

a) The volume of output at which both the locations have the same profit​ is 140

Explanation:

We are looking for the quantity produced that give us the same profit.  

First we have to get the equation of profit in both location.

Profit function

P(x) =Revenue- Total cost P(x) =(Px * Q)-(FC + vc*Q)

Where  

FC=Fixed cost

vc=unitary variable cos

Q=produce quantity

Px=Price

Q=produce quantity

Bonham Profit

P(x) =(Px * Q)-(FC + vc*Q)

P(x) =(29000 * Q)-(820000 + 13000*Q)

McKinney Profit

P(x) =(29000 * Q)-(960000 + 12000*Q)

To find the Q where both profit are equal

(29000 * Q)-(820000 + 13000*Q)=(29000 * Q)-(960000 + 12000*Q)

29000 * Q-820000 -13000*Q=29000 * Q-960000 - 12000*Q

We put all the numbers multiple by Q in the same term

29000 * Q-29000* Q -13000*Q - 12000*Q=820000 -960000

-1000*Q=-140000

Q=140