Question 71) What is the optimal solution to the problem described in Table 10-6?

71) What is the optimal solution to the problem described in Table 10-6?

A) X1 = 50; X2 = 0

B) X1 = 30; X2 = 20

C) X1 = 20; X2 = 30

D) X1 = 25; X2 = 25

E) X1 = 0; X2 = 25

72) Goal programming and linear programming differ in that

A) in LP, the objective function is maximized or minimized, while in goal programming, the deviation between goals and possible achievement is minimized.

B) slack variables are used in LP, while deviational variables are used in goal programming.

C) deviational variables have positive objective function coefficients in goal programming, but slack variables have 0 coefficients in LP.

D) All of the above

E) None of the above

73) A goal programming problem had two goals (with no priorities assigned). Goal number 1 was to achieve a cost of $3,600 and goal number 2 was to complete the task in 400 hours or fewer. The optimal solution to this problem resulted in a cost of $3,600 and a completion time of 420 hours. What was the value for the objective function for this goal programming problem?

A) 400

B) -400

C) 20

D) 0

E) None of the above

74) Agile Bikes has manufacturing plants in Salt Lake City, Dallas, and Chicago. The bikes are shipped to retail stores in Los Angeles, New York, Miami, and Seattle. Information on shipping costs, supply, and demand is given in the following table:

What type of mathematical programming is required to solve this problem?

A) Linear programming

B) Integer programming

C) Mixed-integer programming

D) Zero-one integer programming

E) Nonlinear programming

Table 10-7

The Elastic Firm has two products coming on the market: Zigs and Zags. To make a Zig, the firm needs 10 units of product A and 15 units of product B. To make a Zag, they need 20 units of product A and 30 units of product B. There are only 2,000 units of product A and 3,200 units of product B available to the firm. The profit on a Zig is $4 and on a Zag it is $6. Management objectives in order of their priority are:

(1) Produce exactly 50 Zigs.

(2) Achieve a target profit of at least $750.

(3) Use all of the product B available.

Let X1 = number of Zigs, X2 = number of Zags.

d1- = underachievement of Zig goal

d1+ = overachievement of Zig goal

d2- = underachievement of profit target

d2+ = overachievement of profit target

d3- = unused product B

d3+ = additional amount of product B needed

75) In the goal programming problem described in Table 10-7, what is the objective function?

A) Min: P1d1- + P1d1+ + P2d2+ + P2d2- + P3d3- + P3d3+

B) Min: P1d1- + P1d1+ + P2d2+ + P3d3+

C) Min: P1d1- + P1d1+ + P2d2- + P3d3-

D) Min: P1d1- + P2d2- + P3d3-

E) Min: P1d1+ + P2d2+ + P3d3+

76) In the goal programming problem described in Table 10-7, how is the goal of producing exactly 50 Zigs expressed?

A) X1 + d1+ = 50

B) X1 – d1+ = 50

C) X1 + d1- = 50

D) X1 – d1- = 50

E) X1 + d1- – d1+ = 50

77) In the goal programming problem described in Table 10-7, how is the goal of achieving a target profit of at least $750 expressed?

A) X1 + X2+ d2- = 750

B) X1 + X2+ d2– d2+ = 750

C) 4X1 +6 X2+ d2-= 750

D) 4X1 + 6X2+ d2– d2+ = 750

E) X1 + X2- d2+ = 750

78) In the goal programming problem described in Table 10-7, how is the goal of the use of all product B available expressed?

A) 15X1 + 30X2+ d3– d3+ = 3200

B) X1 + X2+ d3– d3+ = 3200

C) X1 + X2+ d3-= 3200

D) 15X1 + 30X2+ d3-= 3200

E) 15X1 + 3-X2- d3+ = 3200

79) In the goal programming problem described in Table 10-7, what is the optimal solution?

A) X1 = 75 + X2= 91.67

B) X1 = 91.67 + X2= 50

C) X1 = 50 + X2= 75

D) X1 = 50 + X2= 91.67

E) X1 = 75 + X2= 50

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