Please include steps and be accurate Thank you so much The cost of producing and
ID: 1945254 • Letter: P
Question
Please include steps and be accurate
Thank you so much
The cost of producing and selling a certain item is $220x + $15,000 for the first 1,000 units, $120x + $115,000 for a production range between 1,000 and 2,500 units, and $60x + $265,000 for more than 2,500 units, where x is the number of units produced. Assume the selling price is $200 per unit and all units produced are sold. What is the break even production level? What is the level of production that will maximize profit? If only 90% of the units produced are sold, what is the break even point? What is the optimal production level for (c)?Explanation / Answer
First 1000
Cost = 220*1000 +15000 = 235000
100% Sales = 200*1000 = 200000
90% Sales = 90% * 200000 = 180000
1000 to 2500
Cost = 120*1500 +115000 = 295000
100% Sales = 200*1500 = 300000
90% Sales = 90% * 200000 = 270000
First 2500
Cost = 235000 + 295000 = 530000
100% Sales = 200000 + 300000 = 500000
90% Sales = 90% * 500000 = 450000
Till 2500 units, cost is always greater than sales so break even doesnt occur
if units sold above 2500
cost = 530000 + 265000 + 60x = 795000 + 60x
100% Sales = 500000 + 200x
90% Sales = 450000 + 200x*90% = 450000 + 180x
for break even at 100% sales
cost = sales
795000 + 60x = 500000 + 200x
x = 295000/140 = 2107.14
break even after this at 2108
total units sold = 2500 + 2108 = 4608
for break even at 90% sales
cost = sales
795000 + 60x = 450000 + 180x
x = 345000/120 = 2875
total units sold = 2500 + 2875 = 5375
for 100% sales
profit maximizes at infinity as the fixrd cost per good goes down.
but profit margin = (sales - cost)/sales = 1 - (795000 + 60x)/(500000 + 200x)
note that x is units sold above 2500
for 90% sales
profit maximizes at infinity as the fixrd cost per good goes down.
but profit margin = (sales - cost)/sales = 1 - (795000 + 60x)/(450000 + 180x)
note that x is units sold above 2500
the optimal production level has no finite value as more the goods produces more profit (ever additional unit produced adds 200 -60 = 140 to profit (and 180 -60 = 120 in case of 90% sales))
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