how do you solve applications of linear equations

Question

Cost function C(x)=ax+b     Cost is expenditure)

x=# items purchased, C=C(x)=cost of x items, a= unit cost, b= fixed cost

 

EX. 1  Let C(x)=220+8000=manafacturers cost to produce x bicycles

(a)  Fixed cost=C(0)=

(b) Unit cost =cost for 1 additional item

      Unit cost = C(1)- C(0)= ^c/^x=C2-C1/X2-X1=C(q)-C(p)/q-p

Find the cost to produce 40 bicycles

how many bicycles was produced if the cost was $30,000

Answer 1

C(x) = 220x +8000

the fixed cost is 8000. This is how much is spent regardless of the number of bicycles produced

the unit cost is 220. This is how much additional money is spent to produce each bicycle.

 

C(40) = cost to produce 40 bicycles = 220(40) + 8000 = 16,800

 

If C(x) = 30,000 = 220x + 8000

then 220x = 22000

x = 100 bicycles

 

You could also find how many bicycles were produces if the cost was $30,000 this way.

 

The difference in cost between $30,000 and $16,800 is $13,200, which is the additional cost of the additional bicycles beyond 40.

 

So we divide 13,200/220 = 60 more bicycles

So the total is 40 + 60 = 100 bicycles (same answer)

 

Answer 2

C(x) = 220x + 8000

 

So when you look at this equation you can find the first three answers by substituting x and solving

 

C(0) means replace x with a zero

 

C(0) = 220(0) + 8000

        =   0 + 8000

        =   8000   - this is your fixed cost

 

Now do the same thing to find C(1)

 

then find C(1) - C(0)  to get your unit cost

 

the cost of 40 bicycles

 

would be C(40)  - just substitute 40 for x

 

and to find how many bicycles you can produce for $30,000

 

C(x) = $30,000

 

$30,0000 = 220x + 8000  - use this equation to solve for x (number of bicycles)

 

hope this helps