Optimization and model

1. What is the optimal value of x?

1. What is the optimal value of y?

2)The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the weekly profit when producing the optimal amounts?

Multiple Choice

• $0.

• $900.

• $800.

3)

1. What is the optimal value of x?

1. What is the optimal value of y?

4) 

Find the values of x1 and x2 where the following two constraints intersect. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

1. (1) 5x1 + 7x2 ≥ 59

2. (2) 3x1 + 3x2 ≥ 13

5)

Use the graphical method for linear programming to find the optimal solution for the following problem.

Minimize C = 6x + 10y

subject to 2x + 4y ≥ 12

                5x + 2y ≥ 10

and       x ≥ 0, y ≥ 0.

Top of Form

Multiple Choice

• (x, y) = (0, 0)

• (x, y) = (0, 3)

• (x, y) = (0, 5)

• (x, y) = (1, 2.5)

• (x, y) = (6, 0)

• 6) 

Based on the following sensitivity report, how much should the firm be willing to pay for 162 more units of Resource_C?

Variable Cells

Constraints

(Round your answer to 2 decimal places.)

Bottom of Form

7)

Based on the following sensitivity report, what would be the change in the objective function value if the objective function coefficient for Product_2 increases to 16?

Variable Cells

Constraints

(Round your answer to the nearest whole number.)

8)Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient?

Variable Cells

Constraints

• Product_2

• Product_1

• Product_3

9) Variable cells

Constraints

If the right-hand side of Resource B changes to 80, then the objective function value:

Top of Form

Multiple Choice

• can only be discovered by resolving the problem.

• will decrease by $1,500.

• will decrease by $750.

• will decrease by $2,250.

• will remain the same.

• 10)Variable cells

  Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
  $B$6	Activity 1			30	23	17
  $C$6	Activity 2			40	50	10
  $D$6	Activity 3		–7	20		1E+30

• Constraints

  Cell	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
  $E$2	Resource A	20	7.78	20	10	12.5
  $E$3	Resource B	30		30	50	10
  $E$4	Resource C	18		40	1E+30	22

•  

• If the coefficients of Activity 1 and Activity 2 in the objective function are both increased by $10, then:

• Multiple Choice

  • the optimal solution remains the same.

  • the optimal solution will change.

  • the optimal solution may or may not remain the same.

  • the shadow prices are valid.

  • None of the choices is correct.

11)Variable cells 

If the coefficients of Activity 1 and Activity 2 in the objective function are both increased by $10, then:

Top of Form

Multiple Choice

Bottom of Form

• the optimal solution remains the same.

• the optimal solution will change.

• the optimal solution may or may not remain the same.

• the shadow prices are valid.

• None of the choices is correct.

• 12) Variable cells 

  Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
  $B$6	Activity 1			30	23	17
  $C$6	Activity 2			40	50	10
  $D$6	Activity 3		–7	20		1E+30

• Constraints

  Cell	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
  $E$2	Resource A	20	7.78	20	10	12.5
  $E$3	Resource B	30		30	50	10
  $E$4	Resource C	18		40	1E+30	22

• 
  If the right-hand side of Resource A changes to 10, then the objective function value:

• Multiple Choice

• will decrease by $77.80.

• will decrease by $12.50.

• will decrease by $125.

• can only be discovered by resolving the problem.

• will remain the same.

• 13)Variable cells

  Cell	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
  $B$6	Activity 1			30	23	17
  $C$6	Activity 2			40	50	10
  $D$6	Activity 3		–7	20		1E+30

• Constraints

  Cell	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
  $E$2	Resource A	20	7.78	20	10	12.5
  $E$3	Resource B	30		30	50	10
  $E$4	Resource C	18		40	1E+30	22

• 
  If the coefficient for Activity 1 in the objective function changes to $40, then the objective function value:

• Multiple Choice

• will remain the same.

• will increase by $77.80.

• can only be discovered by resolving the problem.

• will increase by $30.

• will increase by $23.

14) A shadow price reflects which of the following in a maximization problem?

• The marginal cost of adding additional resources.

• The marginal gain in the objective value realized by adding one unit of a resour

• The marginal loss in the objective value realized by adding one unit of a resource.

• The marginal gain in the objective value realized by subtracting one unit of a resource.

• None of the above