Question

A company can make 12 printing presses for $78,600. It can make 19 printing presses for $82,380. Find the linear equation that models the cost to produce x printing presses. Use slope-intercept form

Answer 1

`C(x) = 540x + 72120`

Explanation:

Given

Cost = $78,600 when Printing Press = 12

Cost = $82,380 when Printing Press = 19

Required

Determine the linear equation

From the given parameters; Cost is a function of Printing Press

Represent Cost by C and Printing press by x;

This implies that C = f(x)

The given parameters can then be modeled as;
`(x, C)`

`(x_1, C_1) = (12,78600)`

`(x_2, C_2) = (19,82380)`

The first step is to calculate the slope, m;

`m = (C_1 - C_2)/(x_1 - x_2)`

`m = (78600 - 82380)/(12 - 19)`

`m = (-3780)/(-7)`

`m = 540`

The linear equation can then be calculated using slope formula

`m = (C- C_2)/(x - x_2)`

Substitute 540 for m and
`(x_2, C_2) = (19,82380)`

`540 = (C- 82380)/(x - 19)`

Multiply both sides by x - 19

`540 * (x-19)= (C- 82380)/(x - 19) * (x-19)`

`540 * (x-19)= C- 82380`

Open bracket

`540x - 10260 = C - 82380`

Add 82380 to both sides

`540x - 10260 + 82380= C - 82380 + 82380`

`540x - 10260 + 82380= C`

`540x + 72120= C`

`C = 540x + 72120`

Hence;

`C(x) = 540x + 72120`