Copyright 2019 Pearson Education, Inc.

1-1 Copyright © 2019 Pearson Education, Inc.

Chapter One: Management Science

PROBLEM SUMMARY

1.Total cost, revenue, profit, and break-even 2.Total cost, revenue, profit, and break-even 3.Total cost, revenue, profit, and break-even 4.Break-even volume 5.Graphical analysis (1−2) 6.Graphical analysis (1−4) 7.Break-even sales volume 8.Break-even volume as a percentage of capacity (1−2) 9.Break-even volume as a percentage of capacity (1−3) 10.Break-even volume as a percentage of capacity (1−4) 11.Effect of price change (1−2) 12.Effect of price change (1−4) 13.Effect of variable cost change (1−12) 14.Effect of fixed cost change (1−13) 15.Break-even analysis 16.Effect of fixed cost change (1−7) 17.Effect of variable cost change (1−7) 18.Break-even analysis 19.Break-even analysis 20.Break-even analysis; profit analysis 21.Break-even analysis; indifference (1−20) 22.Break-even analysis 23.Break-even analysis; volume and price analysis 24.Break-even analysis 25.Break-even analysis 26.Break-even analysis; profit analysis 27.Break-even analysis; price and volume analysis 28.Break-even analysis; profit analysis 29.Break-even analysis; profit analysis 30.Break-even analysis; profit analysis 31.Break-even analysis 32.Multiproduct break-even analysis 33.Decision analysis 34.Expected value 35.Linear programming 36.Linear programming 37.Linear programming 38.Linear programming 39.Forecasting/statistics 40.Linear programming 41.Waiting lines 42.Shortest route

PROBLEM SOLUTIONS

1.a)== ==

= + = + =

= = =

= − =

f v fv

300, $8,000,

$65 per table, $180;

TC $8,000 (300)(65) $27,500;

TR (300)(180) $54,000;

$54,000 27,500 $26,500 per month vc cp c vc vp Z

• f

v 8,000 69.56 tables per month

180 65

c v pc = = =

−−

2.a)fv fv

12,000, $18,000, $0.90,

$3.20;

TC

18,000 (12,000)(0.90)

$28,800;

TR (12,000)($3.20) $38, 400;

$38, 400 28,800 $9,600 per year v cc p c vc vp Z = == = =+ =+ = = ==

= − =

• f

v

18,000

7,826

3.20 0.90

= ==

−−

c v pc 3.a)= == =

= + = +=

= ==

= − = −

fv fv

18,000, $21,000, $.45,

$1.30;

TC $21,000 (18,000)(.45) $29,100;

TR (18,000)(1.30) $23,400;

$23,400 29,100 $5,700 (loss) v cc p c vc vp Z b)

4.= = =

= = =

−−

fv f v

$25,000, $.40, $.15,

25,000

100,000 lb per month

.40 .15

c p c c v pc f v

21,000

24,705.88 yd per month

1.30 .45

c v pc = = =

−−

Introduction to Management Science 13e Bernard W. Taylor (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) All Chapters/ Supplement files download link at the end of this file. 1 / 4

1-2 Copyright © 2019 Pearson Education, Inc.

5.

6.

7. −−

f v

$25,000

= = = 1,250 dolls 30 10 c v pc

• Break-even volume as percentage of capacity

7,826

.652 65.2%

12,000

= = = =

v k

9. = = = =

Break-even volume as percentage of capacity

24,750.88

.988 98.8%

25,000

v k

10. = = = =

Break-even volume as percentage of

100,000

capacity .833 83.3%

120,000

v k

• f

v

18,000

9,729.7cupcakes

2.75 0.90

It increases the break-even volumefrom 7,826 to 9,729.7 per year.c v pc = = =

−−

12. = = =

−−

f v

25,000

55,555.55 lb

.60 .15

per month; it reduces the break-even volume from 100,000 lb per month to 55,555.55 lb.c v pc

• f

v

25,000

65,789.47 lb

.60 .22

per month;it increases the break-even volume from 55,555.55 lb per month to 65,789.47 lb per month.c v pc = = =

−−

14. = = =

−−

f v

39,000

102,613.57 lb

.60 .22

per month; it increases the break-even volume from 65,789.47 lb per month to 102,631.57 lb per month.c v pc

• fv

f v

Initial profit: (9,000)(.75)

4,000 (9,000)(.21) 6,750 4,000 1,890

$860 per month; increase in price:

(5,700)(.95) 4,000 (5,700)(.21) 5,415

4,000 1,197 $218 per month; the dair Z vp c vc Z vp c vc

= − − = −

− = − − =

= − −

= − − = −

−=y should not raise its price.

16. −

f v

35,000

= = = 1,750

30–10

c v pc The increase in fixed cost from $25,000 to $35,000 will increase the break-even point from 1,250 to 1,750 or 500 dolls; thus, he should not spend the extra $10,000 for advertising.

• Original break-even point (from problem 7) = 1,250

New break-even point: = = =

−−

f v

17,000

1,062.5

30 14 c v pc

Reduces BE point by 187.5 dolls.

• a) = = =

−−

f v

$27,000

5,192.30 pizzas

8.95 3.75

c v pc

• =

5,192.3

259.6 days 20

c) Revenue for the first 30 days = 30(pv − vcv)

= 30[(8.95)(20) −

(20)(3.75)]

= $3,120

$27,000 − 3,120 = $23,880, portion of fixed cost not recouped after 30 days. = = =

−−

f v

$23,880

New 5,685.7 pizzas

7.95 3.75

c v pc

• / 4

1-3 Copyright © 2019 Pearson Education, Inc.Total break-even volume = 600 + 5,685.7 = 6,285.7 pizzas 5,685.7 Total time to break-even 30 20 314.3 days =+ =

• a) Cost of Regular plan = $55 + (.33)(260 minutes)

= $140.80

Cost of Executive plan = $100 + (.25)(60 minutes)

= $115

Select Executive plan.

• 55 + (x − 1,000)(.33) = 100 + (x − 1,200)(.25)

− 275 + .33x = .25x − 200 x = 937.50 minutes per month or 15.63 hrs.

• cf = $26,000

cv = $0.67 ($5.36/8 = 0.67) p = $3.75 = −

26,000

3.75 0.67

v = 8,442 slices Forecasted annual demand = (540)(52) = 28,080

Z = $91,260 – 44,813.6 = 46,446.4

21.OLD New 26,000 + (.67)v = 30,000 + (.48)v .19v = 4,000 v = 21,053 slices Z = New profit – old profit

Z = $47,781.60 – 46,446.40

= $1,335.20

Purchase equipment

• a) =

− 7,500

14,000

.35p p = $0.89 to break even

b) If the team did not perform as well as expected

the crowds could be smaller; bad weather could reduce crowds and/or affect what fans eat at the game; the price she charges could affect demand.

c) This will be a subjective answer, but $1.25 seems

to be a reasonable price.Z = vp − cf − vcv

Z = (14,000)(1.25) − 7,500 − (14,000)(0.35)

= 17,500 − 12,400

= $5,100

• a) cf = $1,700

cv = $12 per pupil p = $75 = − 1,700 75 12 v

= 26.98 or 27 pupils

b) Z = vp − cf − vcv

$5,000 = v(75) − $1,700 − v(12) 63v = 6,700 v = 106.3 pupils

c) Z = vp − cf − vcv

$5,000 = 60p − $1,700 − 60(12) 60p = 7,420 p = $123.67

• a) cf = $350,000

cv = $12,000 p = $18,000 = − f v c v pc = −

350,000

18,000 12,000

= 58.33 or 59 students

b) Z = (75)(18,000) − 350,000 − (75)(12,000)

= $100,000

c) Z = (35)(25,000) − 350,000 − (35)(12,000)

= 105,000

This is approximately the same as the profit for 75 students and a lower tuition in part (b).

• p = $400

cf = $8,000 cv = $75

Z = $60,000 +

= − f v Zc v pc + = −

60,000 8,000

400 75

v

v = 209.23 teams

• Fixed cost (cf) = 875,000

Variable cost (cv) = $200 Price (p) = (225)(12) = $2,700 v = cf/(p – cv) = 875,000/(2,700 – 200)

= 350 3 / 4

1-4 Copyright © 2019 Pearson Education, Inc.

With volume doubled to 700:

Profit (Z) = (2,700)(700) – 875,000 – (700)(200)

= $875,000

• Fixed cost (cf) = 100,000

Variable cost (cv) = $(.50)(.35) + (.35)(.50) + (.15)(2.30)

= $0.695

Price (p) = $6 Profit (Z) = (6)(45,000) – 100,000 – (45,000)(0.695)

= $138,725

This is not the financial profit goal of $150,000.The price to achieve the goal of $150,000 is, p = (Z + cf + vcv)/v

= (150,000 + 100,000 + (45,000)(.695))/45,000

= $6.25

The volume to achieve the goal of $150,000 is, v = (Z + cf)/(p − cv)

= (150,000 + 100,000)/(6 − .695)

= 47,125

• a) Monthly fixed cost (cf) = cost of van/60 months
• labor (driver)/month

= (21,500/60) + (30.42

days/month)($8/hr) (5 hr/day)

= 358.33 + 1,216.80

= $1,575.13

Variable cost (cv) = $1.35 + 15.00

= $16.35

Price (p) = $34 v = cf/(p − vc)

= (1,575.13)/(34 − 16.35)

v = 89.24 orders/month

• 89.24/30.42 = 2.93 orders/day − Monday through

Thursday Double for weekend = 5.86 orders/day − Friday through Sunday Orders per month = approximately (18 days) (2.93 orders) + (12.4 days)(5.86 orders) = 125.4 delivery orders per month Profit = total revenue − total cost = vp – (cf + vcv)

= (125.4)(34) − 1,575.13 – (125.4)(16.35)

= 638.18

• a)

==

−−

f v 500 30 14 c v pc v = 31.25 jobs

• (8 weeks)(6 days/week)(3 lawns/day) = 144

lawns

Z = (144)(30) − 500 − (144)(14)

Z = $1,804

• (8 weeks)(6 days/week)(4 lawns/day) = 192 lawns

Z = (192)(25) − 500 − (192)(14)

Z = $1,612

No, she would make less money than (b)

• a) ==

−−

f v 700 35 3 c v pc v = 21.88 jobs

• (6 snows)(2 days/snow)(10 jobs/day) = 120 jobs

Z = (120)(35) − 700 − (120)(3)

Z = $3,140

• (6 snows)(2 days/snow)(4 jobs/day) = 48 jobs

Z = (48)(150) − 1800 − (48)(28)

Z = $4,056

Yes, better than (b)

d) Z = (120)(35) − 700 − (120)(18)

Z = $1,340

Yes, still a profit with one more person

• cf = $7,500

Monthly cf = ($2,300)(12)

= $27,600

Total cf = $35,100 cv = 0 p = $0.24 f c v p

35,100

= = = 146,250 hits per year .24 v = 12,188 hits per month $45,000 = v(.24) – (12)(3,500) – (0)v .24v = 87,000 v = 362,500 v = 30,208 hits per month

• This is a “multiproduct” break-even problem.

The formula for the break-even volume is, =

   

−   

   

v Total fixed cost weighted average weighted average selling price variable cost =

+ − +

18,000

[(3.20)(.70) (2.50)(.30)] [(.90)(.70) (.45)(.30)]

v

v = 8,089.89 units

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