latisha works for a fashion company. she wants to know the potential profits of a new purse. the company…

latisha works for a fashion company. she wants to know the potential profits of a new purse. the company spent $25,000 designing the purse. additionally, each purse costs $5 to make and send to stores. latisha’s company wants to sell each purse for $45. p = number of purses sold t = net profit after all expenses which function models the net profit based on the number of purses sold? t = 40p - 25,000 t = 25,000 - 50p t = 25,000 + 40p t = 50p - 25,000

latisha works for a fashion company. she wants to know the potential profits of a new purse. the company spent $25,000 designing the purse. additionally, each purse costs $5 to make and send to stores. latisha’s company wants to sell each purse for $45. p = number of purses sold t = net profit after all expenses which function models the net profit based on the number of purses sold? t = 40p - 25,000 t = 25,000 - 50p t = 25,000 + 40p t = 50p - 25,000

Answer

Explanation:

Step1: Calculate revenue

Revenue from selling $p$ purses at $45$ dollars each is $45p$.

Step2: Calculate cost

Cost includes a fixed - cost of $25000$ and a variable cost of $5p$ (since each purse costs $5$ to make and send). So total cost is $25000 + 5p$.

Step3: Calculate net profit

Net profit $t$ is revenue minus cost. So $t=45p-(25000 + 5p)$. Simplify the expression: [ \begin{align*} t&=45p-25000 - 5p\ t&=(45p-5p)-25000\ t&=40p - 25000 \end{align*} ]

Answer:

$t = 40p-25000$