42000 and it costs 1242000 to produce 1000 units and the owner wants to sell each unit for 1200?
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The fixed cost is independent of the number of units made. The variable cost depends on the number of units made. If it costs 1242000 to produce 1000 units, then the unit cost price is 1242. So the cost of production is C=42000+1242N where N is the number of units made. The owner sells each unit for 1200 so if he sells N units his sales will be 1200N. His profit is sales - total cost = 1200N-1242N-42000=-42N-42000 which is a loss because it costs him more to make the units than he's getting in sales.

However, if the cost of unit production includes the fixed cost then we need to deduct the fixed cost from 1242000 to work out the cost price per unit: 1242000-42000=1200000, making the unit cost 1200, the same as the selling price, and therefore he will never cover the fixed cost, no matter how many units he sells.

If he were to change the selling price from 1200 to S, SN-1200N-4200 is the profit. The break-even figure is when SN-1200N=42000, so N(S-1200)=42000. If he is to break even at N=1000, then S-1200=42, and S=1242. For N>1000, the profit would be 1242N-1200N-42000=42N-42000=42(N-1000), that is, 42 for each unit sold beyond 1000 units.

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