# solving linear equation

### solving linear equation

I'm confused about how write linear equations to find the answers to the following:

Cost to make 3 items is \$125, cost to make 7 is \$125.

A. Assume liner relationship, determine rule for the cost C of making products s

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### Re: solving linear equation

A. Let C(x) be the cost function.
the general form of C(x)= ax+b where a is the variable cost, x is the number of items and b is the fixed cost.
Here, 125=3a+b …..(1)
125=7a+b ….(2)
Suntracting (2) from (1) we get -4a=0 i.e. a=0 i.e. therefore b=125
i.e. C(x)=125

B. Revenure function: R(x)=25x where \$25 is the selling price.

C. Profit Function: P(x)=R(x)-C(x)=25x-125

D. Break even Point:
R(x)=C(x) is the condition to find break event i.e. then there is no profit or loss.
25x=125 so, x=5

So if 5 items are sold i.e. when x=5 she will make neither profit nor loss which is break even point.

stephenwoodford

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