a company produces n units of a product per month, where (c(x)) represents the total cost and (r(x))…

a company produces n units of a product per month, where (c(x)) represents the total cost and (r(x)) represents the total revenue for the month. the functions are modeled by (c(x)=250x + 600) and (r(x)=-0.75x^{2}+400x - 500). the profit is the difference between revenue and cost where (p(x)=r(x)-c(x)). what is the total profit, (p(x)), for the month?\n1. (p(x)=-0.75x^{2}+150x - 100)\n2. (p(x)=-0.75x^{2}-150x + 100)\n3. (p(x)=-0.75x^{2}+150x - 1100)\n4. (p(x)=-0.75x^{2}-150x + 1100)

a company produces n units of a product per month, where (c(x)) represents the total cost and (r(x)) represents the total revenue for the month. the functions are modeled by (c(x)=250x + 600) and (r(x)=-0.75x^{2}+400x - 500). the profit is the difference between revenue and cost where (p(x)=r(x)-c(x)). what is the total profit, (p(x)), for the month?\n1. (p(x)=-0.75x^{2}+150x - 100)\n2. (p(x)=-0.75x^{2}-150x + 100)\n3. (p(x)=-0.75x^{2}+150x - 1100)\n4. (p(x)=-0.75x^{2}-150x + 1100)

Answer

Explanation:

Step1: Recall profit formula

$P(x)=R(x)-C(x)$ Given $R(x)= - 0.75x^{2}+400x - 500$ and $C(x)=250x + 600$.

Step2: Substitute functions

$P(x)=(-0.75x^{2}+400x - 500)-(250x + 600)$

Step3: Expand and simplify

$P(x)=-0.75x^{2}+400x - 500 - 250x-600$ $P(x)=-0.75x^{2}+(400x - 250x)+(-500 - 600)$ $P(x)=-0.75x^{2}+150x - 1100$

Answer:

$P(x)=-0.75x^{2}+150x - 1100$ (Option 3)