Question

Consider the following information as part of a breakeven analysis:

1. Cost of Production:

   Number of Units	Cost ($)
   0	o
   700	4,900

2. Cost of Buying

Number of Units	Cost ($)
0	1,500
700	3,600

• What would be the equation for the production cost?
• What would be the equation for the buying cost?
• What is the breakeven # Unis?
• What is the breakeven amout?
• If you were only interested in 400 units, which option should be selected?
• If you were only interested in 200 units, which option should be selected?

Answer 1

a. Let the equation for the cost of production be CP(q) = A + Bq

When q = 0, CP(0) = 0 => A + B*0 = 0 => A = 0

When q = 700, CP(700) = 4,900 => B*700 = 4,900 => B = 4,900/700 => B = 7

Therefore, the equation for the cost of production is, CP(q) = 7q

b. Let the equation for the cost of buying be CB(q) = C + Dq

When q = 0, CB(0) = 1,500 => C + D*0 = 1,500 => C = 1,500

When q = 700, CB(700) = 3,600 => 1,500 + D*700 = 3,600 => 700D = 2,100 => D = 3

Therefore, the equation for the cost of buying is, CB(q) = 1500 + 3q

c & d.

At break-even point, CB(q) = CP(q)

=> 1500 + 3q = 7q

=> 1500 = 4q

=> q = 1500/4

=> q = 375

Therefore, break-even quantity = 375 units

Break-even amount = 7*375 = $2,625

e. If q = 400 units

CP(400) = 7*400 = $2,800

CB(400) = 1500 + 3*400 = 1500 + 1200 = $2,700 (Cost of buying is less than the cost of production)

If you are only interested in 400 units, you should buy the good.

f. If q = 300 units

CP(400) = 7*200 = $1,400

CB(400) = 1500 + 3*200 =1500 + 600 = $2,100 (Cost of buying is more than the cost of production)

If you are only interested in 200 units, you should produce the good.