A pharma company produces two types of Active Pharmaceutical Ingredients (API), API T and API C. Many biochemical materials are usually necessary to produce a small amount of APIs. To produce 1kg of API T, one must use 5kg and 10kg of biochemical materials Wand P, respectively. To produce 1kg of API C, one must use 4 kg and 5 kg of biochemical materials W and P, respectively. It costs $100 and $60 to produce 1kg API T and C, respectively. The pharma company can spend $600 at most to produce the APIs. Taking into account yield uncertainties of the APIs, the pharma company has two goals as follows. Goal 1: The total amount of biochemical material W should be 35kg or more (i.e., approximately 35kg, ideally more than 35kg. In the worst case, the amount is less than 35kg.) Goal 2: The total amount of biochemical material P should be 60kg or less (i.e., approximately 60kg, ideally less than 60kg. In the worst case, the amount is more than 60kg.) The pharma company must determine how much API T and API C, respectively, should be produced. (a) Clearly define decision variables and deviation variables (b) Write all constraints using decision variables and deviation variables defined in part (a). (c) Suppose that Goal 1 and Goal 2 are priority level 1 and 2 goals, respectively. Write the objective function for this goal programming. (d) Find the optimal production amount of API T and API C by solving the goal programming with the constraints and objective function defined in question (c). You must clearly show how you find the optimal solution.
A pharma company produces two types of Active Pharmaceutical Ingredients (API), API T and API C. Many biochemical materials are usually necessary to produce a small amount of APIs. To produce 1kg of API T, one must use 5kg and 10kg of biochemical materials Wand P, respectively. To produce 1kg of API C, one must use 4 kg and 5 kg of biochemical materials W and P, respectively. It costs $100 and $60 to produce 1kg API T and C, respectively. The pharma company can spend $600 at most to produce the APIs. Taking into account yield uncertainties of the APIs, the pharma company has two goals as follows. Goal 1: The total amount of biochemical material W should be 35kg or more (i.e., approximately 35kg, ideally more than 35kg. In the worst case, the amount is less than 35kg.) Goal 2: The total amount of biochemical material P should be 60kg or less (i.e., approximately 60kg, ideally less than 60kg. In the worst case, the amount is more than 60kg.) The pharma company must determine how much API T and API C, respectively, should be produced. (a) Clearly define decision variables and deviation variables (b) Write all constraints using decision variables and deviation variables defined in part (a). (c) Suppose that Goal 1 and Goal 2 are priority level 1 and 2 goals, respectively. Write the objective function for this goal programming. (d) Find the optimal production amount of API T and API C by solving the goal programming with the constraints and objective function defined in question (c). You must clearly show how you find the optimal solution.
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter3: Introduction To Linear Programming
Section: Chapter Questions
Problem 40RP
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Transcribed Image Text:A pharma company produces two types of Active Pharmaceutical Ingredients (API), API T and API C.
Many biochemical materials are usually necessary to produce a small amount of APIs. To produce
1kg of API T, one must use 5kg and 10kg of biochemical materials Wand P, respectively. To produce
1kg of API C, one must use 4 kg and 5 kg of biochemical materials Wand P, respectively. It costs
$100 and $60 to produce 1kg API T and C, respectively. The pharma company can spend $600 at
most to produce the APIs. Taking into account yield uncertainties of the APIs, the pharma company
has two goals as follows.
Goal 1: The total amount of biochemical material W should be 35kg or more (i.e., approximately 35kg,
ideally more than 35kg. In the worst case, the amount is less than 35kg.)
Goal 2: The total amount of biochemical material P should be 60kg or less (i.e., approximately 60kg,
ideally less than 60kg. In the worst case, the amount is more than 60kg.)
The pharma company must determine how much API T and API C, respectively, should be produced.
(a) Clearly define decision variables and deviation variables
(b) Write all constraints using decision variables and deviation variables
defined in part (a).
(c) Suppose that Goal 1 and Goal 2 are priority level 1 and 2 goals, respectively.
Write the objective function for this goal programming.
(d) Find the optimal production amount of API T and API C by solving the goal programming with
the constraints and objective function defined in question (c). You must clearly show how you
find the optimal solution.
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