I need a step by step solution for the following. 5. A manufacturing plant has a

Question

I need a step by step solution for the following.

5. A manufacturing plant has a potential production capacity of 1,000 units per month (capacity can be increased by 10 percent if subcontractors are employed). The plant is normally operated at about 80 percent of capacity. Operating the plant above this level significantly increases variable costs per unit because of the need to pay the skilled workers higher overtime wage rates. For output levels up to 80 percent of capacity, variable cost per unit is $100. Above 80 percent and up to 90 percent, variable costs on this additional output increase by 10 percent. When output is above 90 percent and up to 100 percent of capacity, the additional units cost an additional 25 percent over the unit variable costs for outputs up to 80 percent of capacity. For production above 100 percent and up to 110 percent of capacity, extensive subcontracting work is used and the unit variable costs of these additional units are 50 percent above those at output levels up to 80 percent of capacity. At 80 percent of capacity, the plant’s fixed costs per unit are $50. Total fixed costs are not expected to change within the production range under consideration. Based on the preceding information, complete the following table.

Q

TTC

TFC

TVC

ATC

AFC

AVC

MC

500

600

700

800

900

1000

1100

Q

TTC

TFC

TVC

ATC

AFC

AVC

MC

500

600

700

800

900

1000

1100

Explanation / Answer

Working notes:

(1) 80% capacity = 1,000 x 80% = 800 units

(90% capacity = 900 units, 100% capacity = 1,000 units and 110% capacity = 1,100 units)

(2) TFC = AFC x Q = $50 x Q

TFC = $50 x 800 = $40,000

(3) Upto 800 units, AVC = $100

(4) For 900 units, AVC = $100 x 1.1 = $110

(5) For 1,000 units, AVC = $100 x 1.25 = $125

(6) For 1,100 units, AVC = $100 x 1.5 = $150

(7) TVC = AVC x Q

(8) TC = TFC + TVC

(9) ATC = TC / Q

(10) MC = Change in TC / Change in Q

(11) All values except Q are in dollars.

Therefore:

Q TC TFC TVC ATC AFC AVC MC 500 90,000 40,000 50000 180 50 100 180 600 1,00,000 40,000 60000 166.67 50 100 100 700 1,10,000 40,000 70000 157.14 50 100 100 800 1,20,000 40,000 80000 150 50 100 100 900 139000 40,000 99000 154.44 50 110 190 1000 165000 40,000 125000 165 50 125 260 1100 205000 40,000 165000 186.36 50 150 400

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