Problem 2 Central Critical Chemical (CCC) manufactures three chemicals: A, B and C. These hemicals are produced via two production processes: 1 and 2. • Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C. • Running process 2 for an hour costs $1 and yields 2 units of A and 1 unit of B. o meet customer demand, at least 6 units of A, 3 units of B, and 1 unit of C must be produced aily. Suppose you are asked to formulate an LP model for CCC to determine an optimal daily roduction plan (i.e., how many hours should CCC run process 1 and how many hours should CCC un process 2 each day) that minimizes the total cost. (a) Write down LP model and clearly define the decision variables, the objective function, and constraints. (b) Solve the LP model using the graphical method.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.3: Assignment Models
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Problem 2 Central Critical Chemical (CCC) manufactures three chemicals: A, B and C. These
chemicals are produced via two production processes: 1 and 2.
• Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C.
• Running process 2 for an hour costs $1 and yields 2 units of A and 1 unit of B.
To meet customer demand, at least 6 units of A, 3 units of B, and 1 unit of C must be produced
daily. Suppose you are asked to formulate an LP model for CCC to determine an optimal daily
production plan (i.e., how many hours should CCC run process 1 and how many hours should CCC
run process 2 each day) that minimizes the total cost.
(a) Write down LP model and clearly define the decision variables, the objective function, and
constraints.
(b) Solve the LP model using the graphical method.
(c) Provide a justification on why the divisibility assumption holds for the problem.
Transcribed Image Text:Problem 2 Central Critical Chemical (CCC) manufactures three chemicals: A, B and C. These chemicals are produced via two production processes: 1 and 2. • Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C. • Running process 2 for an hour costs $1 and yields 2 units of A and 1 unit of B. To meet customer demand, at least 6 units of A, 3 units of B, and 1 unit of C must be produced daily. Suppose you are asked to formulate an LP model for CCC to determine an optimal daily production plan (i.e., how many hours should CCC run process 1 and how many hours should CCC run process 2 each day) that minimizes the total cost. (a) Write down LP model and clearly define the decision variables, the objective function, and constraints. (b) Solve the LP model using the graphical method. (c) Provide a justification on why the divisibility assumption holds for the problem.
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Linear programming, often known as linear optimization, is a method for obtaining the best result (such as the highest profit or the lowest cost) in a mathematical model using linear criteria.

Linear programming is a method for determining the most optimal solution to a problem given constraints. Using linear programming, we convert our real-world issue into a mathematical model. It is made up of a goal function, linear inequalities, and constraints.

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