A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example): Max 10x1 + 12x2 – 100y1 – 200y2 s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1} 2x1 + 5x2 ≤ 2500 {Constraint 2} 2x1 + 1x2 ≤ 300 {Constraint 3} My1 ≥ x1 {Constraint 4} My2 ≥ x2 {Constraint 5} yi={1, if product j is produced ; 0, otherwise} Which of the constraints limit the amount of raw materials that can be consumed? A. Constraint 3 B. Constraint 4 C. Constraint 5 D. Constraint 3 and 4 E. Constraint 1, 2, and 3
A bakery produces both pies and cakes. Both products use the same materials (flour, sugar and eggs) and both have a setup cost ($100 for cakes, $200 for pies). The baker earns a profit of $10 per cake and $12 per pie and can sell as many of each as it can produce. The daily supply of flour, sugar and eggs is limited. To manage the decision-making process, an analyst has formulated the following linear programming model (assume that it is possible to produce fractional pies and cakes for this example):
Max 10x1 + 12x2 – 100y1 – 200y2
s.t. 5x1 + 10x2 ≤ 1000 {Constraint 1}
2x1 + 5x2 ≤ 2500 {Constraint 2}
2x1 + 1x2 ≤ 300 {Constraint 3}
My1 ≥ x1 {Constraint 4}
My2 ≥ x2 {Constraint 5}
yi={1, if product j is produced ; 0, otherwise}
Which of the constraints limit the amount of raw materials that can be consumed?
A. Constraint 3
B. Constraint 4
C. Constraint 5
D. Constraint 3 and 4
E. Constraint 1, 2, and 3
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