A smart phone company plans to produce and sell \( p \) smart phones. The cost of producing \( p \) phones is given by \( 265,000+150 p \) in dollars. The company receives \( \$ 400 \) on the sale of each phone, so the revenue for selling \( p \) phones is given by \( 400 p \). For what value of \( p \) is the revenue equal to the cost? A) 500 B) 840 C) 1060 D) 1200

To find the value of \( p \) at which the revenue equals the cost, we set the revenue equal to the cost: \[ \text{Revenue} = \text{Cost} \] That is, \[ 400p = 265,000 + 150p \] To solve for \( p \), subtract \( 150p \) from both sides: \[ 400p - 150p = 265,000 \] This gives us: \[ 250p = 265,000 \] Now, divide both sides by 250: \[ p = \frac{265,000}{250} = 1060 \] So, the value of \( p \) is 1060. The correct answer is C) 1060. Now let’s have some more fun with this! Did you know that the first smartphone, IBM's Simon Personal Communicator, launched in 1994? It had a touchscreen, email capability, and even apps (though they were pretty primitive by today’s standards). It’s fascinating to see how far the industry has come since then! When it comes to maximizing profits, companies often confuse fixed and variable costs in their calculations. A common mistake is to overlook how increased production can lead to rising costs due to inefficiencies or lower quality if not managed well. Always keep an eye on those details to stay ahead!