The objective of the company is to maximize profits by producing the optimal mix of components.
There are six constraints on the production process. These constraints are as follows:
Use of the shaper machine is limited to 7,200 minutes
Use of the grinder machine is limited to 6,600 minutes
Maximum production of Component A is 1,000 because that is all that can be sold
Minimum production of Component A is 600 because the company has order in hand for that quantity
Maximum production of Component B is 1,000 because that is all that can be sold
Maximum production of Component C is 200 because that is all that can be sold
The decision variables are the production levels for the three components. Therefore, there are three decision variables, as follows:
Production quantity of Component A stated in units
Production quantity of Component B stated in units
Production quantity of Component C stated in units
Objective Function in Terms of Decision Variables
The objective function is "Profit" on production. Thus, Profit = Profit Contribution of Component A + Profit Contribution of Component B + Profit Contribution of Component C. In each case, Profit Contribution = Units Produced times Profit Contribution per unit ($8 Component A; $6 Component B; and $9 Component C).
Constraints in Terms of Decision Variables
The constraints involve machine use and production limits. The constraints are as follows:
(Units of Component A times 6 minutes)+(Units of Component B times 4 minutes)+(Units of Component C times 4 minutes) < 7,200 shaper machine minutes
(Units of Component A times 4 minutes)+(Units of Component B times 5 minutes)+(Units of Component C times 2 minutes) < 6,600 grinder machine minutes
Units produced of Component A < 1,000
Units produced of Component B < 1,000
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