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Problem: Formulate and solve the following production lincar programming problem Production Rates in Hours Per Unit ProductProduct ProductProduct Production Hours Available Department 0.10 0.10 0.12 0.12 0.05 400 400 500 450 400 0.05 0.15 0.12 0.10 0.20 0.06 0.03 Stamping Drilling Assembly Finishing Packaging 0.06 0.05 0.03 0.02 0.04 1000 6000 $10 $6 500 3000 $16 $11 100 1000 $20 $14 Sales minimum unit? Potentialmaximum 500 $25 $15 Net Selling Price/Unit Variable Cost/Unit Only 2000 square feet of the type of sheet metal used for products 2 and 4 will be available during the month. Product 2 requires 2.0 square feet per unit and product 4 uses 1.2 square feet per unit. Find the optimal production level of products 1 to 4 such that the net profit will be maximized. https://d2vlcm61l7u1fs.cloudfront.net/media%2F29f%2F29fac592-04dd-44ed-9b1f-ea23b08543a4%2Fphpgf7wif.png

Decision variable –
X = Product 1 unit
Y = Product 2 unit
Z = Product 3 unit
W = Product 4 unit
Objective function –
Net profit of Product 1 = 10 (profit) – 6 (cost) = 4
Net profit of Product 2 = 25 (profit) – 15 (cost) = 10
Net profit of Product 3 = 16 (profit) – 11 (cost) = 5
Net profit of Product 4 = 20 (profit) – 14 (cost) = 6
Objective is to maximize profit
Maximize –
4X + 10Y + 5Z + 6W
Constraints –
1) Hrs available for Stamping
0.03 * X + 0.15 * Y + 0.05 * Z + 0.1 * W
 
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