Three divisions of the Twinsburg Company manufacture a product in which each com

Question

Three divisions of the Twinsburg Company manufacture a product in which each complete unit consists of four units of component A and three units of component B. The two components (A and B) are manufactured from two different raw materials. There are 100 units of raw material 1 and 200 units of raw material 2 available. Each of the three divisions uses a different method for manufacturing the components, resulting in different raw-material requirements per production run in each division and the number of each component produced by that run.

Input/Run (units)

RAW MATERIAL

Output/Run (units)

A

B

For example, each production run at Division 1 requires 8 units of raw material 1 and 6 units of raw material 2. The output form this run is 7 units of A and 5 units of B. As Production Manager, formulate a model to determine the number of production runs for each division that maximizes the total number of completed units of the final product.

Input/Run (units)

RAW MATERIAL

Output/Run (units)

A

B

Explanation / Answer

let the number of production runs in the 3 divisions be x,y,z

no of units of A produced = 7x+6y+8z

no of units B produced = 5x+9y+4z

no of units of the final product = 4(7x+6y+8z)+3(5x+9y+4z)

we need to maximize this 4(7x+6y+8z)+3(5x+9y+4z)

subject to the constraints

8x+5y+3z 100   (material 1)

6x+9y+8z 200 (material 2)

and x,y,z 0

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.