Question

The cost of producing iPhones can be linearly related to the number of iPhones produced. If 100 iPhones are produced, the cost is $102,500, and if 2000 iPhones are produced, the cost is $150,000.

Part A: Find the equation for the cost of producing iPhones.
Part B: Due to the mass production of iPhones, Apple has noticed a perpendicular decline in iPods in relation to iPhones. Find the equation that shows this decline if 100 iPods are produced for the cost of $120,000.
Part C: A sister company wants to create a knock-off iPhone using a model that is parallel to Apple's iPhone production. However, their production is significantly less expensive. They can produce 1000 knock-off iPhones at the cost of $25,000. Find the equation for the cost of producing knock-off iPhones.

A) Part A: Cost = 47.5x - 4500, Part B: Cost = -0.25x + 14500, Part C: Cost = 25x
B) Part A: Cost = 47.5x + 4500, Part B: Cost = 0.25x + 14500, Part C: Cost = 25x
C) Part A: Cost = 4500x + 47.5, Part B: Cost = -14500x + 0.25, Part C: Cost = 25x
D) Part A: Cost = 47.5x - 4500, Part B: Cost = -0.25x - 14500, Part C: Cost = 25x

Answer 1

To solve Part A, calculate the slope using two given cost-quantity pairs, then determine the y-intercept to form the linear cost equation for iPhone production.

Step-by-step explanation:

The question involves finding linear equations based on given costs and production quantities. Part A requires us to find the equation for the cost of producing iPhones given two cost-quantity pairs. The cost ($C$) of producing $x$ iPhones is a linear function in the form $C = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

We can use the given pairs (100, $102,500) and (2000, $150,000) to solve for $m$ and $b$. The slope $m$ is calculated using the change in cost divided by the change in quantity. The y-intercept $b$ is then found by substituting $m$ and one of the points into the equation.