The cost of buying computer chips is $2/piece for the first 100 and $1.75/piece beyond that. Write an expression for the cost of p chips and draw a graph of the function.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The cost of the first 100 computer chips is $2/piece and the chips bought after that are for $1.75 each.

For p chips the cost function is

`C(p) = 2*p` for `p<= 100 `

`C(p) =` `200 + (p - 100)*1.75` for `p > 100` .

The graph of the function is:

It can be seen that the slope of the graph is 2 initially and reduces to 1.75 after 100.

jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

Let Y is the total cost in $ and X be the number of chips you buy.

Then for your first 100 chips;

Y= 2*X  (X<=100)------------(1)

For chips more than 100 you will definitely pay 200$ for first 100. The rest you will pay 1.75$ each. So the equation valids only when X is beyond 100.

Y = 200+(x-100)*1.75  ; (X>100)-------(2)

OR

Y = 100*2+(x-100)*1.75  ; (X>100)-----(2)

 

When plotting the graphs (1) plots only from X=0 to X=100

This is a simple y=mx type graph. This graph start through cordinate(0,0) and ends at (100,200)

If you connect these two points you will get the graph.

 

When plotting grapgh (2) it plots when X>100

It is a y=mx+c type graph. This graph start through cordinate (101,201.75) and end cannot be set. But the graph will pass the point (110,217.5)

From (101,201.75) you can draw a line which also goes through (110,217.5) which will give you the graph.

 

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