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The Home Times Company is about to launch a new line of coffee tables. The graph on the right shows the cost to make the coffee tables and the revenue the company will receive from the sale.
[tex] \red{{\mathsf{{{{{{ A.} }}}}} }}[/tex] Use the graph to write an equation for the cost, C and the revenue, R.
[tex] \red{{\mathsf{{{{{{ B.} }}}}} }}[/tex] How much will it cost to make 10 coffee tables? 20 coffee tables? 30 coffee tables? you may use either the graph or the equation to find the answer.
[tex] \red{{\mathsf{{{{{{ C.} }}}}} }}[/tex] What revenue will the sale for 10,20 and 30 coffe tables bring? how much money will the company make or lose in each case.
[tex] \red{{\mathsf{{{{{{ D.} }}}}} }}[/tex] How many coffee tables must be produced and sold so that the cost the revenue are the same? Name the coordinates of the point where this will happen.
[tex] \red{{\mathsf{{{{{{ E.} }}}}} }}[/tex] Why do you think {50, 20 000} is called the "break - even point.
[tex] \sf\huge { Answer \: Solution}[/tex]
[tex] \red{{\mathsf{{{{{{ A.} }}}}} }}[/tex]
- Use the graph to write an equation for the cost, C and the revenue, R.
The Equation for the Cost or C:
[tex] \sf\large Y-intercept = 10 000 \\ \\ \sf\large Slope: m \: \frac{20000 \: - \: 1000 }{50 \: - \: 0} \\ \\ = 200 \\ \\ \sf\large \red{{\mathsf{{{{{{ c \: = \: 10000 + 200x} }}}}} }}[/tex]
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[tex] \green{{\mathsf{{{{{{ A.} }}}}} }}[/tex] This is the Equation for the Revenue, R:
[tex]\sf\large y - intercept \: = \: 0 \\ \\ \sf\large slope \: m \: = \: 40 0 \\ \\ \sf\large \red{{\mathsf{{{{{{ r \: = \: 400 \times } }}}}} }}[/tex]
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[tex] \green{{\mathsf{{{{{{B. } }}}}} }}[/tex]
- How much will it cost to make 10 coffee tables? 20 coffee tables? 30 coffee tables? you may use either the graph or the equation to find the answer.
For 10 coffee tables: C = 10,000 + 200(10) = Php 12,000.00
For 20 coffee tables: C = 10,000 + 200(20) = Php 14,000.00
For 30 tables: C = 10,000 + 200(30) = Php 16,000.00
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[tex] \green{{\mathsf{{{{{{C. } }}}}} }}[/tex]
- What revenue will the sale for 10,20 and 30 coffe tables bring? how much money will the company make or lose in each case.
For 10 coffee tables: R = R = 400(10) = Php 4,000.00
For 20 coffee tables: R = 400(20) = Php 8,000.00
For 30 coffee tables: R = 400(30) = Php 12,000.00
- The company will lose Php 8,000.00 if only 10 coffee tables are produce and solid. On the other hand, it will gain Php 6,000.00 if 20 coffee tables are produced and sold and Php 4,000.00 if 30 coffee tables are produced.
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[tex] \green{{\mathsf{{{{{{D. } }}}}} }}[/tex]
- How many coffee tables must be produced and sold so that the cost the revenue are the same? Name the coordinates of the point where this will happen.
For the Cost, C = 10,000 + 200x and the Revenue, R = 400x to the same, equate the two equations:
- 10,000 + 200x = 400x
- x = 50
This means that the company must produce and sell 50 coffee tables for the cost and the Revenue to be the same.
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[tex] \green{{\mathsf{{{{{{E. } }}}}} }}[/tex]
- Why do you think {50, 20 000} is called the "break - even point.
A break even point is the point at which income from sales are exactly equal to the total cost producing and selling goods. The point {50, 20,000} is called the break even point because it is the point at which the business makes no profit but does not suffer loss.
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