4QA3 F12 Week 7 Lecture Notes

33 000 2500200 33 000 900q tc2 q 200 900

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Unformatted text preview: order. o  Incremental discount: the discount is applied only to the number of units above the breakpoint. ●  Unit price becomes relevant: TC = K 4QA3 F12 λ Q + h + cλ Q 2 A. Gandomi 27 C2=.28 C1=.29 Source: Nahmias (2009) 4QA3 F12 28 Source: Nahmias (2009) 4QA3 F12 29 QuanCty 1 - 49 50 - 89 90+ Price $1,400=c0 1,100=c1 900=c2 K = $2,500 h = 0.2c (i = 20%) λ = 200 All- units discount: Cost function " 1400Q for 0 ≤ Q < 50 $ $ C (Q ) = # 1100Q for 50 ≤ Q < 90 $ $ 900Q for 90 ≤ Q % 4QA3 F12 A. Gandomi 30 All- units discount: C(Q) curve C(Q) $97,900 $81,000 $68,600 $55,000 4QA3 F12 A. Gandomi 31 All- units discount: Quantities and costs Qj = 2K λ , j = 0,1, 2 ⇒ Q2 = 74.54, Q1 = 67.41, Q0 = 59.76 Ic j TC j (Q ) = λ c j + Kλ Q + Ic j Q 2 j = 0,1, 2. 2500(200) 67.41 + 0.2(1100) = $234, 832.40 67.41 2 2500(200) 90 TC2 (90) = 200(900) + + 0.2(900) = $193, 655.56 90 2 TC1 (67.41) = 200(1100) + Q* = 90 4QA3 F12 A. Gandomi 32 All- units discount: TC(Q) curve TC(Q) TC0(Q) TC1(Q) TC1(67.41)=$234,832.40 TC2(Q) TC (90)=$193,655.56 2 Q2=74.54 Q0=59.76 4QA3 F12 Q1=67.41 A. Gandomi Op9mal Q* 33 Incremental discount: Cost Function 1, 400Q C (Q ) = for 0 ≤ Q < 50 1, 400(50) + 1,100(Q − 50) = 15, 000 + 1,100Q for 50 ≤ Q < 90 70, 000 + 40(11, 00) + 900(Q − 90) for 90 ≤ Q = 33, 000 + 900Q " 1, 400 for 0 ≤ Q < 50 $ C (Q ) $ = # 1,100 + 15, 000 Q for 50 ≤ Q < 90 Q $ $ 900 + 33, 000 Q for 90 ≤ Q % 4QA3 F12 A. Gandomi 34 Incremental discount: C(Q)Function C(Q) $114,000 $70,000 4QA3 F1...
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