the cost for a company to produce x t - shirts can be modeled by c(x)=21x - 98 and the revenue for selling…

the cost for a company to produce x t - shirts can be modeled by c(x)=21x - 98 and the revenue for selling these shirts can be modeled by r(x)=55x - 2x^{2}. which function represents the companys total profit after selling x shirts? (recall that profit equals revenue minus cost.)\na. p(x)=-2x^{2}-34x + 98\nb. p(x)=2x^{2}-34x + 98\nc. p(x)=-2x^{2}+34x + 98\nd. p(x)=2x^{2}+34x - 98

the cost for a company to produce x t - shirts can be modeled by c(x)=21x - 98 and the revenue for selling these shirts can be modeled by r(x)=55x - 2x^{2}. which function represents the companys total profit after selling x shirts? (recall that profit equals revenue minus cost.)\na. p(x)=-2x^{2}-34x + 98\nb. p(x)=2x^{2}-34x + 98\nc. p(x)=-2x^{2}+34x + 98\nd. p(x)=2x^{2}+34x - 98

Answer

Answer:

A. $P(x)=-2x^{2}-34x + 98$

Explanation:

Step1: Recall profit formula

$P(x)=R(x)-C(x)$

Step2: Substitute given functions

$P(x)=(55x - 2x^{2})-(21x - 98)$

Step3: Distribute the negative sign

$P(x)=55x - 2x^{2}-21x + 98$

Step4: Combine like - terms

$P(x)=-2x^{2}+(55x-21x)+98=-2x^{2}-34x + 98$