10. Jingle Bells Inc. has received a rush order for as many of two types of Easter eggs as can be purchased and shipped during a 2-week period. Preliminary analysis by Jingle Bells indicates that the profit on this order is related to the number of each type of Easter egg manufactured by the function: P(x1 , x2) = – x12– x22 + 12x1 + 10x2 + 61 where x1 = thousands of units of Type 1 eggs and x2 = thousands of units of Type 2 eggs. Because of other commitments over the two weeks, Jingle Bells has available only 60 hours in the Shipping and Packaging Department to get the order out the door. It is estimated that every 1000 units of Type 1 eggs will require 20 hours in the department and every 1000 units of Type 2 eggs will require 30 hours. i) Formulate a mathematical model that can be used to determine how many thousands of each Type of egg should be manufactured in the two-week period so as to maximise profit. ii) Find a solution to your mathematical model.
10. Jingle Bells Inc. has received a rush order for as many of two types of Easter eggs as can be purchased and shipped during a 2-week period. Preliminary analysis by Jingle Bells indicates that the profit on this order is
related to the number of each type of Easter egg manufactured by the function:
P(x1 , x2) = – x12– x22 + 12x1 + 10x2 + 61
where x1 = thousands of units of Type 1 eggs and x2 = thousands of units of Type 2 eggs. Because of other commitments over the two weeks, Jingle Bells has available only 60 hours in the Shipping and Packaging Department to get the order out the door. It is estimated that every 1000 units of Type 1 eggs will require 20 hours in the department and every 1000 units of Type 2 eggs will require 30 hours.
i) Formulate a mathematical model that can be used to determine how many thousands of each Type of egg should be manufactured in the two-week period so as to maximise profit.
ii) Find a solution to your mathematical model.
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