##### Document Text Contents

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16) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is

infinite, then profits are unbounded.

Answer: FALSE

17) The reduced cost (shadow price) for a positive decision variable is .

Answer: zero

18) The sensitivity range for a is the range of values over which the

quantity values can change without changing the shadow price

Answer: constraint quantity Diff: 2

19) is the analysis of the effect of parameter changes on the optimal solution.

Answer: Sensitivity analysis

20) The sensitivity range for a constraint quantity value is also the range over which the

is valid.

Answer: shadow price

21) The sensitivity range for an coefficient is the range of

values over which the current optimal solution point (product mix) will remain optimal.

Answer: objective function

Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX 50R + 75S

s.t.

1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤

300 paint (hours)

.16R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:

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a)Profit would increase by $25. B)Profits would decrease by $25. C) Profits would

increase by $6.25.

d) Profits would decrease by $6.25 e)Cannot tell from the information provided.

Answer: C

79) Aunt Anastasia is planning for next spring, and she is considering making only 2 products. Based on the

results from the linear program, which two products would you recommend that she make?

a) baskets and eggs b)baskets and rabbits c)eggs and rabbits d)She should

continue to make all 3.

e) Cannot tell from the information provided.

Answer: B

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros

requires 2 minutes of machine time, 20 minutes of labor, and costs $10. Brand Bling requires

2..5 minutes of machine time, 30 minutes of labor, and costs $14 to produce. Brand Curious

requires 3 minutes of machine time, 45 minutes of labor, and costs $18 to produce. There are 300

machining hours available per week, 3,750 labor hours, and he has a budget of $3,000. Brand

Astro sells for $15, Brand Bling for $18, and Brand Curious for $25.

The LP formulation that maximizes week profit shown below.

MAX 15A +18B + 25 C

s.t.

2A + 2.5B + 3C ≤ 300

20A + 30B + 45C ≤ 3,750

10A + 14B + 18C ≤ 3,000

The solution from QM for Windows is show below.

16) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is

infinite, then profits are unbounded.

Answer: FALSE

17) The reduced cost (shadow price) for a positive decision variable is .

Answer: zero

18) The sensitivity range for a is the range of values over which the

quantity values can change without changing the shadow price

Answer: constraint quantity Diff: 2

19) is the analysis of the effect of parameter changes on the optimal solution.

Answer: Sensitivity analysis

20) The sensitivity range for a constraint quantity value is also the range over which the

is valid.

Answer: shadow price

21) The sensitivity range for an coefficient is the range of

values over which the current optimal solution point (product mix) will remain optimal.

Answer: objective function

Consider the following linear program, which maximizes profit for two products, regular (R), and super (S):

MAX 50R + 75S

s.t.

1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤

300 paint (hours)

.16R + 0.4 S ≤ 100 inspection (hours)

Sensitivity Report:

Page 16

a)Profit would increase by $25. B)Profits would decrease by $25. C) Profits would

increase by $6.25.

d) Profits would decrease by $6.25 e)Cannot tell from the information provided.

Answer: C

79) Aunt Anastasia is planning for next spring, and she is considering making only 2 products. Based on the

results from the linear program, which two products would you recommend that she make?

a) baskets and eggs b)baskets and rabbits c)eggs and rabbits d)She should

continue to make all 3.

e) Cannot tell from the information provided.

Answer: B

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros

requires 2 minutes of machine time, 20 minutes of labor, and costs $10. Brand Bling requires

2..5 minutes of machine time, 30 minutes of labor, and costs $14 to produce. Brand Curious

requires 3 minutes of machine time, 45 minutes of labor, and costs $18 to produce. There are 300

machining hours available per week, 3,750 labor hours, and he has a budget of $3,000. Brand

Astro sells for $15, Brand Bling for $18, and Brand Curious for $25.

The LP formulation that maximizes week profit shown below.

MAX 15A +18B + 25 C

s.t.

2A + 2.5B + 3C ≤ 300

20A + 30B + 45C ≤ 3,750

10A + 14B + 18C ≤ 3,000

The solution from QM for Windows is show below.