Question

Lillian is a business woman of manufacturing phones. she must pay a daily fixed cost to rent the building and equipment and also pays a cost per phone produced for materials and labor. let c represent the total cost in dollars of producing p phones in a given day. the table below has select values showing the linear relationship between p and c. determine fixed cost for rent and equipment?

P: 2,4,6
C: 1200, 1400, 1600

Answer 1

1000 dollars

Explanation:

Given

P: ---2 -----,4 ----,6

C: 1200, 1400, 1600

Required

Calculate the fixed cost

First, we need to determine the equation that determines the relationship between P and C

We start by selecting any two corresponding values of P and C

We have that:

`(P_1,C_1) = (2,1200)`

`(P_2,C_2) = (6,1600)`

Calculate the slope, using:

`m = (C_2 - C_1)/(P_2 - P_1)`

`m = (1600 - 1200)/(6 - 2)`

`m = (400)/(4)`

`m = 100`

The equation is then calculated using:

`C - C_2 = m(P - P_2)`

Where

`m = 100` and

`(P_2,C_2) = (6,1600)`

`C - 1600 = 100(P - 6)`

`C - 1600 = 100P - 600`

Collect Like Terms

`C = 100P - 600 +1600`

`C = 100P + 1000`

From the equation above,

100P represents the amount paid for P phones produced

1000 represents the fixed cost paid

C represents the total amount paid