Business Math Problems and Solutions

Posted on Feb 4, 2025 in Naval Architecture and Marine Systems Engineering

Chapter 1

11) For most products… d=800-10p

a) d=800-10(20)=600, d=800-10(70)= 100

b) d=800-10(26)=540, d=800-10(27)=260, d=800-10(68)=120, d=800-10(69)=110

c) TR=d*p, TR=800-10(p)

d) 800-10p^2, 800(30)-10(30)^2= 15000, 800(40)-10(40)^2= 16000, 800(50)-10(50)^2=15000

e) TR/p=d*p/p, d=tr/p, d=16000/40= 400 units

13) Micromedia offers…

a) 9600+120x

b) p=600x-(9600+120x)=480x-9600

c) 480(30)-9600=4800

d) p=480x-9600=0, x=20 students

15) Preliminary… TR=d*P, BE=R-(FC+VC), TR=300,000x

a) 300,000-(4,500,000+150,000x)=30boxes=BE

b) 150,000(50)-4,500.000=$3,000,000, 50 boxes

Chapter 2

2.) Coffee houses… data not true to be equally likely, more pref for others

16.)a.55*.35=.19

b..55+.35-.19=.71

c.1-.71=.29

17.)a)196/989=19%

b.177/196=90%

c.177/989=17.8%

d.177/759=23%

e.(759/989)+(196/989)-(177/989)=78%

Chapter 4

4. Amy decided

a) lease w/lowest cost, chance #of miles she’ll drive

b) Hepburn Honda:36000 miles (12000 miles for 3 years): 36($299) + $0.15(36000 – 36000) = $10,764, 45000 miles (15000 miles for 3 years): 36($299) + $0.15(45000 – 36000) = $12,114,54000 miles (18000 miles for 3 years): 36($299) + $0.15(54000 – 36000) = $13,464, Midtown Motors:36000 miles (12000 miles for 3 years): 36($310) + $0.20*max(36000 – 45000,0) = $11,160.00, 45000 miles (15000 miles for 3 years): 36($310) + $0.20*max(45000 – 45000,0) = $11,160.00, 54000 miles (18000 miles for 3 years): 36($310) + $0.20*max(54000 – 45000,0) = $12,960.00

Hopkins Automotive lease option:36000 miles (12000 miles for 3 years): 36($325) + $0.15*max(36000 – 54000, 0) = $11,700,45000 miles (15000 miles for 3 years): 36($325) + $0.15*max(45000 – 54000, 0) = $11,700, 54000 miles (18000 miles for 3 years): 36($325) + $0.15*max(54000 – 54000, 0) = $11,700

c) Optimistic: 10764, 11160, 11700 Conservative: 13464, 12960,11700

d) EV(Hepburn Honda) = 0.5($10,764) + 0.4($12,114) + 0.1($13,464) = $11,574, EV(Midtown Motors) = 0.5($11,160) + 0.4($11,160) + 0.1($12,960) = $11,340, EV(Hopkins Automotive) = 0.5($11,700) + 0.4($11,700) + 0.1($11,700) = $11,700

f) EV(Hepburn Honda) = 0.3($10,764) + 0.4($12,114) + 0.3($13,464) = $12,114, EV(Midtown Motors) = 0.3($11,160) + 0.4($11,160) + 0.3($12,960) = $11,700, EV(Hopkins Automotive) = 0.3($11,700) + 0.4($11,700) + 0.3($11,700) = $11,700

13. Seneca…

a. Decision: type of grapw to plant, chance: level of demand, consequence: low proft contrib, Alt: plant only ‘C’, only ‘R’, both, chance out: (W,W) (W,S) (S,W) and (S,S).

c) EV (Plant Chardonnay) = 0.55(20) +0.45(70) = 42.5 EV (Plant both grapes) = 0.05(22) + 0.50(40) + 0.25(26) + 0.20(60) = 39.6 EV (Plant Riesling) = 0.30(25) + 0.70(45) = 39.0; Optimal decision: plant chardonnay only

d) Onlr reisling is planted. EV (Plant both grapes) = 0.05(22) + 0.50(40) +0.05(26) + 0.40(60) = 46.4 EV (Plant Riesling) = 0.10(25) + 0.90(45) = 43.0 change plant both grapes

e) only EV too change is Plant Chardonnay, EV (Plant Chardonnay) = 0.55(20) + 0.45(50) = 33.5, too low best to plant both

15. Lake…

a) Decision: Max Cash flow EV (Small)= 0.1(400) + 0.6(500) + 0.3(660) = 538, EV (Medium) =0.1(-250) + 0.6(650) + 0.3(800) = 605, EV (Large) = 0.1(-400) + 0.6(580) + 0.3(990) = 605, build large or medium size

b) if demand is not large enough, best to build medium size