Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - Chapter 7 Test - Page 484: 15

Answer

See below:

Work Step by Step

(a) As, fixed cost is\[\$360,000\], and it will be cost\[\$850\]to produce each computer. It means the fixed cost is a constant parameter, but \[\$850\]is a variable parameter, because it is a cost to produce per computer. Therefore, the total cost will be the sum of variable cost and fixed cost. \[\begin{align} & \text{Total cost}\left( C \right)=\text{ Fixed cost}+\text{Variable cost} \\ & \text{Total cost}\left( C \right)=360,000+850x \\ \end{align}\] where, x denotes the number of computers. (b) Since, the computer will be sold for the cost \[\$1150\]to produce each computer. It means, \[\$1150\]is a variable parameter, because it is the cost to sell per computer. Therefore, total selling cost or total revenue to sell the x computer: \[\begin{align} & \text{Total Revenue}\left( R \right)=\text{Variable selling cost} \\ & \text{Total Revenue}\left( R \right)=1150x \\ \end{align}\] where, x denotes the number of computers. (c) Break-even is the amount of product by which, the company will be in zero profit or zero loss condition. It means, the break-even point is the point at which total selling cost will be equal to total production cost. \[\begin{align} & \text{Total selling cost}\left( R \right)=\text{ Total production cost}\left( C \right) \\ & \text{1150}x=360,000+850x \\ & 300x=360,000 \\ & x=1200 \\ & \end{align}\] Now, \[\begin{align} & \text{Total selling cost}\left( R \right)=1150x \\ & =1150\times 1200 \\ & =1,380,000 \end{align}\] Hence, the break-even point is\[\left( 1200,\text{ }1,380,000 \right)\].
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