I need to write a mathematical expressoin for the function to generate costs of the business for a day.If running cost of a business is $60 per day plus $3 for each product which is made. The...

I need to write a mathematical expressoin for the function to generate costs of the business for a day.

If running cost of a business is $60 per day plus $3 for each product which is made. The maximum products made in a day is 50.

I also need the domain and range, and the inverse of the function.

Expert Answers
kjcdb8er eNotes educator| Certified Educator

Cost/day: C(n) = $60 + $3*n

The domain is the set of input values, in this case the number of products made in a day: 0 to 50.

The range is the corresponding set of output values, in this case the minimum to maximum cost: C(0) to C(50) = 60 to 210.

To get the inverse of this function, solve for n:

C = 60 + 3*n

C - 60 = 3n

(C - 60)/3 = n

neela | Student

If we take the running cost $60 per day and  the cost per unit product is $3 per day, then the cost function C(x) is given by: C(x)=running cost+number units produced*cost per unit of production.So,

C(x) =3*x+60, where x is the number of products manufactured each day.

The domain of x is 0<=x<=50 by the conditions laid down by the problem.

The range of the function C(x) is given by:

0<=C(x)<=50*3+60 or o<=C(x)<=210.

Example: You want to produce 100 units of product on a day. Then the cost ; C(100)= 3*100+60=$360

Inverse function:

Given the cost of a day, the inverse function should give the number of units to be produced.

C(x) = 3x+60

Therefore, x= [C(x)-60]/3. Now replace C(x) by x and x by y to get the inverse function:

y=[x-60]/3 is the inverse of C(x) = 3x+60.

Example:

If 360 is the total cost,  to find the number of units to produce, y= (1/3)(360)-20=120-20 =20