Answered Essay: Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows.

Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows.

Machine
Component Shaper Grinder
1 6 4
2 4 5
3 4 2

The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.

a. Provide the mathematical formulation for this problem. Carefully define your decision variables, objective function, model constraints, and non-negativity statement.

Expert Answer

 

Decision variables:

Let

A = units of component 1 manufactured

B = units of component 2 manufactured

C = units of component 3 manufactured

Objective function:

Objective function is to maximize the profits

Max Z = 8A + 6B + 9C

Constraints:

6A + 4B + 4C <= 7200 (Shaper machine available minutes)

4A + 5B + 2C <= 6600 (Grinder machine available minutes)

C <= 200 (No more than 200 units of component 3 can be sold)

B <= 1000 (Component 2 can be sold up to 1000 units)

A <= 1000 (Component 1 can be sold up to 1000 units)

A>=600 (company already has orders for 600 units of component 1 )

A,B,C>= 0 (Non-negativity costraints)

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