Analysis of a linear programming problem
Step 2: Analyzing problem statement and Model
Shelby shelving manufactures two types of shelves. Shelves go through stamping, forming, and lastly, assembly. Model S and Model LX required different time in the forming and the stamping stage. The forming and stamping machine has a maximum of 800 hours each in a month. The monthly capacity of model S is 1900 units, and the monthly capacity of model LX is 1400 units. Currently, 400 units and 14 00 units are being produced for the two models, respectively. The sale price for Model S and LX is $1800 and $2100, respectively.
The selling price of the shelves cannot be increased, but the management thinks they can sell as much as possible to increase profits. The plant’s engineer suggests to cut back the production of Model S because it brings a loss of $9 per unit. The controller has a contrary opinion that lowering the production of Model S will worsen the profit of the company.
Step 3: Setting up the initial Model
Currently, Shelby has a total monthly profit of $62,000, which results from the production of 400 units of Model S and 1400 units of Model XL.
When e cut back the production of Model S to 200 units, the cost per unit increases to $2,050, which is more than the selling price of $1,800.
Step 4: Developing and using constraints according to lab description
The total units assembled for model S and model LX should not exceed 1,900 units and 1,400 units, respectively.
The total hours used for the two models should not exceed 800 hours in each stage in a month.
Step 5: Applying Solver to solve the problem
Solver found a solution where 1,900 units of Model S and 650 units of model LX care produced, and the total profit is $268,250. The printability of the company has increased by 333%. The engineer was wrong to say that they should cut back the production of Model S, and therefore, the controller was right.