4.14-bo'lim : Biznes ilovalari
5. \(x\) vidjetlarini ishlab chiqarish haftasiga dollarda ishlab chiqarish xarajatlari quyidagicha berilgan:
\[C\left( x \right) = 4000 - 32x + 0.08{x^2} + 0.00006{x^3}\]va vidjetlar uchun talab funksiyasi tomonidan berilgan,
\[p\left( x \right) = 250 + 0.02x - 0.001{x^2}\]\(x = 200\) va \(x = 400\) da marjinal xarajat, marjinal daromad va marjinal foyda nima? Bu raqamlar sizga xarajat, daromad va foyda haqida nimani aytadi?
Yechim
Birinchidan, biz daromad va foyda funktsiyalarini olishimiz kerak. Ushbu bo'lim uchun eslatmalardan bilamizki, bu funktsiyalar:
\[\begin{align*}{\mbox{Revenue : }} & R\left( x \right) = x\,p\left( x \right) = 250x + 0.02{x^2} - 0.001{x^3}\\ {\mbox{Profit : }} & P\left( x \right) = R\left( x \right) - C\left( x \right) = - 4000 + 282x - 0.06{x^2} - 0.00106{x^3}\end{align*}\]2-qadam
Ushbu bo'limdagi eslatmalardan bilamizki, marjinal xarajat, marjinal daromad va marjinal foyda funktsiyalari shunchaki xarajatlar, daromadlar va foyda funktsiyalarining hosilasidir, shuning uchun keling, ulardan boshlaylik.
\[\begin{align*}C'\left( x \right) & = - 32 + 0.16x + 0.00018{x^2}\\ R'\left( x \right) & = 250 + 0.04x - 0.003{x^2}\\ P'\left( x \right) & = 282 - 0.12x - 0.00318{x^2}\end{align*}\]3-qadam
\(x\) ning har bir qiymati uchun marjinal xarajat, marjinal daromad va marjinal foyda, keyin,
\[\require{bbox} \bbox[2pt,border:1px solid black]{\begin{align*}C'\left( {200} \right) & = 7.2 & \hspace{0.75in}R'\left( {200} \right) & = 138 & \hspace{0.5in}P'\left( {200} \right) & = 130.8\\ C'\left( {400} \right) & = 60.8 & \hspace{0.5in}R'\left( {400} \right) & = - 214 & \hspace{0.5in}P'\left( {400} \right) & = - 274.8\end{align*}}\]4-qadam
Ushbu hisob-kitoblardan biz 201 ni ishlab chiqarishni ko'rishimiz mumkinst vidjet taxminan 7,2 dollar turadi va taxminan 138 dollar daromad va 130,8 dollar foyda keltiradi.
Xuddi shunday, 401 ni ishlab chiqarishst vidjet taxminan 60,8 dollar turadi va daromad taxminan 214 dollarga, foyda esa 274,8 dollarga kamayadi.