Answered

IDNLearn.com provides a reliable platform for finding accurate and timely answers. Discover in-depth and trustworthy answers to all your questions from our experienced community members.

The Pear company sells pPhones. The cost to manufacture Iphones isC(x)= -21x^2+52000x + 20940dollars (this includes overhead costs and production costsfor each pPhone). If the company sells pPhones for the maximum price they can fetch, therevenue function will be R(x) = -29x^2+ 196000x dollars.How many pPhones should the Pear company produce and sell to maximimze profit? (Rememberthat profit-revenue-cost)

Sagot :

ANSWER:

900

STEP-BY-STEP EXPLANATION:

Given the cost and revenue functions:

[tex]\begin{gathered} C\mleft(x\mright)=-21x^2+52000x+20940 \\ R\mleft(x\mright)=-29x^2+196000x \end{gathered}[/tex]

The profit is:

[tex]\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=-29x^2+196000x-(-21x^2+52000x+20940) \\ P(x)=-29x^2+196000x+21x^2-52000x-20940 \\ P(x)=-8x^2+144000x-20940 \end{gathered}[/tex]

To maximize we derive the profit function and then set it equal to 0 to solve for x

[tex]\begin{gathered} P^{\prime}(x)=\frac{d}{dx}(-8x^2+144000x-20940) \\ P^{\prime}(x)=-16x+144000 \\ P^{\prime}(x)=0 \\ 0=-16x+144000 \\ 16x=14400 \\ x=\frac{14400}{16} \\ x=900 \end{gathered}[/tex]

To maximize profit, a total of 900 pPhones must be produced and sold.

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.