PowerPoint Presentation

Bachelor in Economics (S.E): ManajemenCourse : Matematika Ekonomi (1507ME06)online.uwin.ac.id

Session Topic : Aplikasi Fungsi Kuadrat (1)

Course: Matematika EkonomiBy Handri Santoso, Ph.DUWIN eLearning Program2ContentPart 1Quadratics & Economics

Part 2How to Maximize Profit

Part 3Penerapan Fungsi Kuadrat

Powered by HarukaEdu.com- 1507ME06-Hal #3Part1: Quadratics & EconomicsQuadratics & Economics: Key ConceptsWere producing units of some good & will sell them all at the same price.

Key concepts:Cost: how much it costs you to produce x units.Revenue: total amount of money brought in. Demand: relationship between price & number of units sold.Profit: whats left over after paying costs.Powered by HarukaEdu.com- 1507ME06-Hal #Now some algebra

x : number of units soldp : priceCost: some fixed overhead plus some amount per unit produced C (x ) = c + bxRevenue: number of units sold times price R(x ) = x pDemand: Common sense: to sell more, lower the price & if you raise the price, youll sell less.A simple model of demand p = mx + b where m is negative.Profit: revenue minus costs: profit = R(x ) C (x )Quadratics & Economics: AlgebraPowered by HarukaEdu.com- 1507ME06-Hal #Quadratics & Economics: Lawnmowers GroupworkPowered by HarukaEdu.com- 1507ME06-Hal #Quadratics & Economics: Lawnmowers Groupwork (Cont.)Demand dikali dgn unit terjual Revenue dikurangi dgn cost (biaya produksi)Powered by HarukaEdu.com- 1507ME06-Hal #Part2: How to Maximize ProfitProfit: Parabolas GroupLet f(x) = 4x2 + 24x + 291. Does the graph of f open up or open down?

2. Rewrite f(x) in standard form.

What 3. are the coordinates of the vertex? 4. is the axis of symmetry?5. is the domain and range of f ?

Find 6. any x-intercepts.7. the y-intercept.

8. Sketch the graph of f.Powered by HarukaEdu.com- 1507ME06-Hal #Profit: Parabolas Group (Cont.)Let f(x) = 4x2 + 24x + 291. Does the graph of f open up or open down? up 2. Rewrite f(x) in standard form. f(x) = 4(x + 3)2 73. What are the coordinates of the vertex? (-3, -7)4. What is the axis of symmetry? x = -35. Whats the domain and range of f ? (-, ) & [7, ] 6. Find any x-intercepts. X = -3 7/27. Find the y-intercept. Y = 298. Sketch the graph of f . Powered by HarukaEdu.com- 1507ME06-Hal #Profit: Graph of f(x) = 4(x + 3)2 7xPowered by HarukaEdu.com- 1507ME06-Hal #Profit: How to Maximize ProfitPowered by HarukaEdu.com- 1507ME06-Hal #Profit: How to Maximize Profit (Cont.)252015105-10-150-5(in 00,000s)51015(in 000s)-50Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: LatihanSelesaikan persamaan kuadrat utk mencari akar-akarnya1. Jika fungsi permintaan P = 1000 Q, tentukanFungsi pendapatan, TR (Total Revenue) Banyak barang yg diproduksi agar pendapatan maksimumPendapatan maksimum yg dapat diperolehPowered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Solusi30252015105-10-150-5(in 0000s)Powered by HarukaEdu.com- 1507ME06-Hal #Part3: Penerapan Fungsi KuadratFungsi Kuadrat: Penerapan & ContohPenerapan Fungsi Kuadrat dalam EkonomiFungsi permintaan, penawaran & keseimbangan pasarPengaruh pajak & subsidi terhadap keseimbangan pasarFungsi biaya, penerimaan (untung, rugi & BEP)

Fungsi permintaan,penawaran & keseimbangan pasarContoh:1. Diketahui:Fungsi penawaran P=20Q2 + 4Q & Fungsi permintaannya P=-2Q2+300Tentukan keseimbangan pasarnya !Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: ContohJawab:20Q2 + 4Q = -2Q2 + 30020Q2 + 4Q + 2Q2 - 300= 022Q2 + 4Q 300 = 0Q12= - b b2- 4ac2aD = b2 - 4ac D =16-4.22.-300 D = 16+26400 = 26.416Q12= - 4 264162.22Q12= - 4 162,25944Q1= 158,529 = 3,60344Q2= -166,529 = -3,78544Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Contoh (Lanjut)P=20Q2 +4Q P=20(3,603)2 + 4(3,603)P=259,632 + 14,412P=274,044Keseimbangan pasar terjadi saatP=274,044 & Q=3,603

2. Diketahui:Fungsi penawaran P=20Q2 + 4Q + 12 & Fungsi permintaannya P=-12Q2+300Tentukan keseimbangan pasarnya !Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Contoh (Lanjut)Jawab:20Q2 + 4Q + 12= -12Q2 + 30020Q2 + 4Q + + 12 + 2Q2 - 300= 032Q2 + 4 Q 288 = 0Q12= - b D2aD = b2 - 4ac D =16-4.32.-288D = 16+36864 = 36880D = 192Q12= - 4 1922.32Q1= 188 = 2,9464Q2= -196 = -3,0644Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Contoh (Lanjut)P=20Q2 + 4Q + 12P=20(2,94)2 + 4(2,94) + 12P=196,632Keseimbangan pasar terjadi pada tingkat harga 196,632 & kuantitasnya 2,94Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Biaya, Penerimaan & BEPFungsi Biaya, Penerimaan & BEPTC= aQ2 + bQ + c C= FCVC=aQ2 +bQ, karena VC dipengaruhi oleh produksiTR = P . Q TC= FC + VC

Contoh:Diketahui:Fungsi permintaan yg dihadapi oleh seorang produsen ditunjukkan oleh persamaan P=30-1,5Q.Tentukan persamaan TRnya ?TR = (30-1,5Q)Q TR = 30Q-1,5Q2Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Contoh1. Data yg berhasil dikumpulkan utk memperkirakan keuntungan maximum dari suatu perusahaan adalah:Fungsi permintaan P=16.000-QBiaya produksi biaya tetap Rp. 40juta &Biaya variabel Rp. 100,-/unit. Ditanya:Berapa keuntungan maximum & terjadi pada tingkat berapa unit?Apakah penerimaan maximum sama dgn keuntungan maximum?Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Contoh (Lanjut)TR= PQTR=(16.000 Q) x Q TR = 16.000Q Q2TR max= -16.000/2(-1) = 8.000

TC = FC +VCTC = 40.000.000 + 100Q

= TR-TC = (16.000Q-Q2) (40.000.000+100Q) = 15.900Q-Q2-40.000.000Q max= -b/2a Q= 7.950Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Latihan1. Harga suatu produk ditunjukkan olehFungsi permintaan P=2.000-0,5QBiaya produksi dipisah menjadi FC sebesar Rp. 1juta &Biaya variabel per-unit VC=2+0,04QDitanya:Berapa keuntungan maximum & terjadi pada tingkat produksi berapa?Apakah penerimaan pada unit keuntungan maximum sama dgn penerimaan pada unit penjualan maximum?Berapa BEPnya?Powered by HarukaEdu.com- 1507ME06-Hal #Fungsi Kuadrat: Latihan2. Berdasarkan hasil survey dari suatu perusahaan diperoleh data:Fungsi penerimaan (TR) = 520Q-2Q2 Fungsi biaya (TC) = 0,5Q2+20Q+3.500Tentukanlah:Keuntungan maksimum pada saat Q?Penerimaan maksimum pada saat Q?BEP pada saat Q?

Powered by HarukaEdu.com- 1507ME06-Hal #ReferenceWisc. Quadratics and Economics. Web: math.wisc.edu.Powered by HarukaEdu.com- 1507ME06-Hal #online.uwin.ac.idAssociate Partners :Powered by HarukaEdu.comCourse : Matematika Ekonomi (1507ME06)

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