A company produces 3 types of industrial solvents (S1, S2, S3) by blending 3 grades of distillates (D1, D2, D3) in different proportions. The selling price per gallon for solvents S1, S2, and S3 are $3.20, $3.00, and $ 2.50, respectively. The cost price per gallon for distillates D1, D2, and D3 are $2.50, $2.40, and $2.20, respectively.The company is contractually obligated to produce at least 500,000 gallons of each solvent. It has 1,000,000 gallons of distillate D1, 900,000 gallons of distillate D2, and 800,000 gallons of distillate D3 available in its inventory. For each solvent, regulations dictate the minimum proportion by volume of distillate D1 required, and the maximum proportion by volume of distillate D3 allowed.There are no restrictions on the proportion of distillate D2. The table below specifies these restrictions and summarizes other relevant information.

The company aims to maximize profits subject to the specified constraints.

Task 1.1. Formulate the problem as a linear programming model. [2 Points]

Decision variables:

Objective Function:

A company produces 3 types of industrial solvents (S1, S2, 53) by blending 3 grades of distillates (D1, D2, D3) in different proportions. The selling price per gallon for solvents S1, $2, and $3 are $3.20, $3.00, and $ 2.50, respectively. The cost price per gallon for distillates D1, D2, and D3 are $2.50, $2.40, and $2.20, respectively. The company is contractually obligated to produce at least 500,000 gallons of each solvent. It has 1,000,000 gallons of distillate D1, 900,000 gallons of distillate D2, and 800,000 gallons of distillate D3 available in its inventory. For each solvent, regulations dictate the minimum proportion by volume of distillate D1 required, and the maximum proportion by volume of distillate D3 allowed. There are no restrictions on the proportion of distillate D2. The table below specifies these restrictions and summarizes other relevant information. Solvent S1 S2 53 Cost Available Selling price $3.20 $3.00 $2.50 Minimum Quantity 500,000 500,000 500,000 Min prop of D1 0.6 0.4 0.2 $ 2.50 1,000,000 Distillate D2 $2.40 900,000 Max prop of D3 0.2 0.5 0.6 $ 2.20 800,000 The company aims to maximize profits subject to the specified constraints. Task 1.1. Formulate the problem as a linear programming model. [2 Points] Decision variables: Objective Function: Subject to Constraints