Hi guys! I reaaly need your help with this question A new graduate has started a

Question

Hi guys! I reaaly need your help with this question

A new graduate has started a business of manufacturing alarm-clock and the setup has a monthly fixed cost of $48,000 and production cost of $8 for each clock manufactured. The clocks sell for $14 each.

Determine the cost function associated with manufacturing X alarm clocks.

Determine the revenue function associated with selling X alarm clocks.

Compute the profit or loss during a month in which 6000 alarm clocks are made and sold.

How many alarm clocks must be manufactured and sold in a month in order to break even?

If now the graduate manufactures additional 4000 alarm clocks above the breakeven quantity, what will be the selling price of each unit to make a total loss of $20,000 from the total production?

Explanation / Answer

Cost Function

C(x) = 48000+8x where x is the unit's produced

Revenue Function

R(x) = 14x Where x is the unit's sold

If 6000 alarm clocks are made and sold.

Cost = 48000+8*6000= $96000

Revenue = 14*6000 =$84000

Loss = $96000 - $84000 = $ 12000

Break Even sales

Cost = Revenue

48000 + 8x = 14x

14x - 8x =48000

6x = 48000

x =8000 units is break even sales

New selling price if additional 4000 alarm clocks above the breakeven quantity

Quantity sold = 8000 +4000 =12000 unit

Cost = $ 48000+8*12000 = $ 144000

Selling price per unit = (Cost + Loss)/Unit sold = (144000+20000)/12000 = $ 13.67 (approx)

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