# ADM 2302 Chapter Notes - Chapter 4: Lincoln Near-Earth Asteroid Research, Chief Operating Officer, List Of Subaru Engines

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Week 4 Extra Problems Solution

CHAPTER 3

LINEAR PROGRAMMING: FORMULATION AND

APPLICATIONS

Problems

3.16 a) This is a cost-benefit-tradeoff problem because it asks you to meet minimum required

benefit levels (number of consultants working each time period) at minimum cost.

b)

c) Let f1 = number of full-time consultants working the morning shift (8 a.m.-4 p.m.),

f2 = number of full-time consultants working the afternoon shift (12 p.m.-8 p.m.),

f3 = number of full-time consultants working the evening shift (4 p.m.-midnight),

p1 = number of part-time consultants working the first shift (8 a.m.-12 p.m.),

p2 = number of part-time consultants working the second shift (12 p.m.-4 p.m.),

p3 = number of part-time consultants working the third shift (4 p.m.-8 p.m.),

p4 = number of part-time consultants working the fourth shift (8 p.m.-midnight).

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Minimize C = ($14 / hour)(8 hours)(f1 + f2 + f3) + ($12/ hour)(4 hours)(p1 + p2 + p3 + p4)

subject to

f1 + p1 ≥ 6

f1 + f2 + p2 ≥ 8

f2 + f3 + p3 ≥ 12

f3 + p4 ≥ 6

f1 ≥ 2p1

f1 + f2 ≥ 2p2

f2 + f3 ≥ 2p3

f3 ≥ 2p4

and f1 ≥ 0, f2 ≥ 0, f3 ≥ 0, p1 ≥ 0, p2 ≥ 0, p3 ≥ 0, p4 ≥ 0.

3.19 a) A1 + B1 + R1 = $60,000

A2 + B2 + C2 + R2 = R1

A3 + B3 + R3 = R2 + 1.40A1

A4 + R4 = R3 + 1.40A2 + 1.70B1

D5 + R5 = R4 + 1.40A3 + 1.70B2

b) Let At = amount invested in investment A at the beginning of year t.

Bt = amount invested in investment B at the beginning of year t.

Ct = amount invested in investment C at the beginning of year t.

Dt = amount invested in investment D at the beginning of year t.

Rt = amount not invested at the beginninf of year t.

Maximize Return = 1.40A4 + 1.70B3 + 1.90C2 + 1.30D5 + R5

subject to A1 + B1 + R1 = $60,000

A2 + B2 + C2 – R1 + R2 = 0

–1.40A1 + A3 + B3 – R2 + R3 = 0

–1.40A2 + A4 – 1.70B1 – R3 + R4 = 0

–1.40A3 – 1.70B2 + D5 – R4 + R5 = 0

and At ≥ 0, Bt ≥ 0, Ct ≥ 0, Dt ≥ 0, Rt ≥ 0.

c)

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