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Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the

  1. Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firms billings. What is the schedule and what is the total billing? Let xij = number of hours from consultant i assigned to client j.
    Max fill in the blank x11 + fill in the blank x12 + fill in the blank x13 + fill in the blank x14 + fill in the blank x21 + fill in the blank x22 + fill in the blank x23
    + fill in the blank x24 + fill in the blank x31 +

    fill in the blank

    x32

    		 + fill in the blank x33 +

    fill in the blank

    x34
    s.t. fill in the blank x11 + fill in the blank x12 + fill in the blank x13 +

    fill in the blank

    x14

    		 fill in the blank
    fill in the blank x21 +

    fill in the blank

    x22

    		 + fill in the blank x23 +

    fill in the blank

    x24

    		 fill in the blank
    fill in the blank x31 +

    fill in the blank

    x32

    		 + fill in the blank x33 + fill in the blank x34 fill in the blank
    fill in the blank x11 + fill in the blank x21 + fill in the blank x31 = fill in the blank
    fill in the blank x12 +

    fill in the blank

    x22

    		 + fill in the blank x32 = fill in the blank
    fill in the blank x13 + fill in the blank x23 + fill in the blank x33 = fill in the blank
    fill in the blank x14 + fill in the blank x24 + fill in the blank x34 = fill in the blank
    xij 0 for all i, j
    Hours Assigned Billing
    Avery-Client A fill in the blank 45 $fill in the blank 46
    Avery-Client B fill in the blank 47 fill in the blank 48
    Avery-Client C fill in the blank 49 fill in the blank 50
    Avery-Client D fill in the blank 51 fill in the blank 52
    Baker-Client A fill in the blank 53 fill in the blank 54
    Baker-Client B fill in the blank 55 fill in the blank 56
    Baker-Client C fill in the blank 57 fill in the blank 58
    Baker-Client D fill in the blank 59 fill in the blank 60
    Campbell-Client A fill in the blank 61 fill in the blank 62
    Campbell-Client B fill in the blank 63 fill in the blank 64
    Campbell-Client C fill in the blank 65 fill in the blank 66
    Campbell-Client D fill in the blank 67 fill in the blank 68
    Total Billing $ fill in the blank 69
  2. New information shows that Avery doesnt have the experience to be scheduled for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule?
    Hours Assigned Billing
    Avery-Client A fill in the blank $fill in the blank
    Avery-Client B
    Avery-Client C
    Avery-Client D
    Baker-Client A
    Baker-Client B
    Baker-Client C
    Baker-Client D
    Campbell-Client A
    Campbell-Client B
    Campbell-Client C
    Campbell-Client D
    Total Billing

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