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Section 3  Formulating Linear Programming Problems 1) A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources. 2) In linear programming, a statement such as “maximize contribution” becomes an objective function when the problem is formulated. 3) In a linear programming formulation, a statement such as “maximize contribution” becomes a(n): A) constraint. B) slack variable. C) objective function. D) violation of linearity. E) decision variable. 4) If cars sell for $500 profit and trucks sell for $300 profit, which of the following represents the objective function? A) Maximize profit = 500C + 300T B) Minimize profit = 500C + 300T C) Maximize profit = 500C – 300T D) Minimize profit = 300T – 500C E) Maximize profit = 800(T + C) 5) A linear programming problem contains a restriction that reads “the quantity of X must be at least three times as large as the quantity of Y.” Which of the following inequalities is the proper formulation of this constraint? A) 3X ≥ Y B) X ≤ 3Y C) X + Y ≥ 3 D) X – 3Y ≥ 0 E) 3X ≤ Y 6) A linear programming problem contains a restriction that reads “the quantity of Q must be no larger than the sum of R, S, and T.” Formulate this as a linear programming constraint. A) Q + R + S + T ≤ 4 B) Q ≥ R + S + T C) Q – R – S – T ≤ 0 D) Q / (R + S + T) ≤ 0 E) Q ≤ R + Q ≤ S + Q ≤ T 7) A linear programming problem contains a restriction that reads “the quantity of S must be no less than one-fourth as large as T and U combined.” Formulate this as a linear programming constraint. A) S / (T + U) ≥ 4 B) S – .25T -.25U ≥ 0 C) 4S ≤ T + U D) S ≥ 4T / 4U E) S ≥ .25T + S ≥ .25U 8) A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm’s goal were to maximize profit, what would be the appropriate objective function? A) Maximize profit = $40Y = $25Z B) Maximize profit = $40Y + $25Z C) Maximize profit = $30Y + $20Z D) Maximize profit = 0.25Y + 0.20Z E) Maximize profit = $50(Y + Z) 9) A linear programming problem contains a restriction that reads “the quantity of X must be at least twice as large as the quantity of Y.” Formulate this as a linear programming constraint. 10) A linear programming problem contains a restriction that reads “the quantity of Q must be at least as large as the sum of R, S, and T.” Formulate this as a linear programming constraint. 11) A linear programming problem contains a restriction that reads “the quantity of S must be no more than one-fourth as large as T and U combined.” Formulate this as a linear programming constraint.

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