select the correct answer.\na mobile virtual reality (vr) headset is being sold at a local department store…

select the correct answer.\na 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:\nc(x)=28.15x + 355.\nhow many vr headsets does the store need to sell to break even?\n\na. 83\nb. 64\nc. 35\nd. 11

select the correct answer.\na 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:\nc(x)=28.15x + 355.\nhow many vr headsets does the store need to sell to break even?\n\na. 83\nb. 64\nc. 35\nd. 11

Answer

Explanation:

Step1: Set up break - even equation

At break - even, revenue equals cost. The revenue from selling $x$ headsets at $33.75$ each is $R(x)=33.75x$, and the cost function is $C(x)=28.15x + 355$. Set $R(x)=C(x)$: $33.75x=28.15x + 355$

Step2: Solve for $x$

Subtract $28.15x$ from both sides: $33.75x-28.15x=28.15x + 355-28.15x$ $5.6x=355$ Then divide both sides by $5.6$: $x=\frac{355}{5.6}\approx63.39$ Since we can't sell a fraction of a headset, and we need to cover the cost, we round up to the next whole number. So $x = 64$.

Answer:

B. 64