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Chapter Sequences; Induction; The Binomial Theorem, Question Problem 18AYU

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The term is equal to . For each term that is in the sequence, we plug in the given value for :
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How many of each type should be prepared in order to maximize profit if a lunch stand makes 1.20 profit on each Caesar salad. On weekday it sells between 40 and 60 chef’s salads and between 35 and 50 Caesar salads. The total number sold has never exceeded 100 salads. The maximum 105 occurs if the lunch stand prepares 60 chef’s salads and 50 Caesar salads. Given information: A lunch stand makes 1.20 profit on each Caesar salad. On weekday it sells between 40 and 60 chef’s salads and between 35 and 50 Caesar salads. The total number sold has never exceeded 100 salads. Calculation: Consider the given information. Let x represents the chef’s salads and y represents Caesar salads. A lunch stand makes 1.20 profit on each Caesar salad. P = 0.75 x + 1.20 y On weekday it sells between 40 and 60 chef’s salads and between 35 and 50 Caesar salads. Thus, 40 ≤ x ≤ 60 and 35 ≤ y ≤ 50 So, the required constrains for the situation is: 40 ≤ x ≤ 60 35 ≤ y ≤ 50 x ≥ 0 , y ≥ 0 Draw the graph as shown below: The vertices are A 40 , 35 , B 60 , 35 , C 60 , 50 and D 40 , 50 . The Objective function: P = 0.75 x + 1.20 y . Determine the value of P at each vertex. Vertex P = 0.75 x + 1.20 y A 40 , 35 P = 0.75 40 + 1.20 35 = 72 B 60 , 35 P = 0.75 60 + 1.20 35 = 87 C 60 , 50 P = 0.75 60 + 1.20 50 = 105 D 40 , 50 P = 0.75 60 + 1.20 50 = 90 The maximum 105 occurs if the lunch stand prepares 60 chef’s salads and 50 Caesar salads.
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Question Text
Chapter Sequences; Induction; The Binomial Theorem, Question Problem 18AYU
TopicAll Topics
SubjectAlgebra 2
ClassClass 12
Answer TypeText solution:1