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Cost Structure And Break-Even Analysis For a Manufacturer In a Multi-Tier Distribution System

Understand cost structures with this homework solution.

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Cost Structure and Break-Even Analysis for a Manufacturer in a Multi-TierDistribution SystemA consumer purchases a computer for $800 from a retailer. If the retailer’s markup is 30 percent andthe wholesaler’s markup is 10 percent, both based ontheir respective selling prices, for what pricedoes the manufacturer sell the product to the wholesaler?Let manufacture sell the product to the wholesaler at $xWholesaler markup the price by 10% and sell it the retailer.So, wholesaler sells the product to retailer at =Wholesaler costprice + markup price= $x +($(10/100)*x)= $x +($0.1*x)= $1.1xRetailer markups its cost price by 30% and sell it to the consumerSo, retailer sells the product to the consumer at =Retailer cost price + markup price= $1.1x + {$(30/100) * 1.1x}= $1.1x + ($0.3 * 1.1 x)= $1.1x + $0.33x= $1.43xHence, the retailer sells the computer at $1.43x to the consumer. But the consumer purchased the computer at$800. Hence, we get$1.43x = $800=> x = $800 / 1.43=> x = $559.44Hence, manufacturer sells the computer at $559.44 to the wholesaler.If the unit variable cost for each computer is $350 and the manufacturer has fixed costs totaling $2million, how many computers must this manufacturer sell to break even? How many must themanufacturer sell to realize a profit of $50 million?I have assumed from previous example that thecost of selling one computer is $559.44.Let manufacturer needs to sell x number of computers to break even.Selling price of x number of computer = $559.44 * x= $559.44xUnit variable cost of one computer = $350Hence, unit variable cost of xcomputers = $350 *x= $350xFixed cost for manufacturing computers = $2,000,000Hence, total cost in manufacturing x number of computers = unit cost of x computers + fixed cost= $350x +$2,000,000To achieve break even cost price should be equal to selling price.Hence, we have$559.44x = $350x +$2,000,000=>$559.44x-$350x = 2,000,000=> $209.44x = 2,000,000=> x =2,000,000 / 209.44=> x = 9549.27Let us assume that manufacturer need to sell x number of computers to earn $50 million.Selling price of one computer = $559.44

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