Question

A mobile virtual reality (VR) headset is being sold at a local department store for $33.75. This is the cost function associated with the headsets, where x represents the number of headsets manufactured and sold: C(x) = 28.15x + 355. How many VR headsets does the store need to sell to break even?

Answer 1

Answer:

63 headsets.

Step-by-step explanation:

It is given that, a mobile virtual reality (VR) headset is being sold at a local department store for $33.75.

Let  x represents the number of headsets manufactured and sold.

So, the revenue function is

$R(x)=33.75x$            ...(i)

The given cost function is

$C(x)=28.15x+355$         ...(ii)

In break even point the value of profit is zero. It means revenue and cost are equal.

$R(x)=C(x)$  

$33.75x=28.15x+355$

$33.75x-28.15x=355$

$5.6x=355$

Divide both sides by 5.6.

$x=\dfrac{355}{5.6}$

$x\approx 63.393$

$x\approx 63$

Therefore, the store need to sell 63 headsets.

Answer 2

Answer:

B. 64

Step-by-step explanation:

$33.75 x 64 = $2160

$28.15 x 64 + $355 = $2156.60

$2160 > $2156.60

Therefore the store is beyond breaking even, and they are $3.40 in the green.