Question 1. Linear Programming Models [9 Points] A company produces 3 types of industrial solvents (S1, S2, S3) by blend

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Question 1. Linear Programming Models [9Points]
A company produces 3 types of industrial solvents (S1, S2, S3)by blending 3 grades of distillates (D1, D2, D3) in differentproportions. The selling price per gallon for solvents S1, S2, andS3 are $5, $4, and $ 3, respectively. The cost price per gallon fordistillates D1, D2, and D3 are $4, $3, and $2, respectively. The company is contractually obligated to produce at least1,000,000 gallons of each solvent. It has 1,000,000 gallons of eachdistillate available in its inventory. For each solvent,regulations dictate the minimum proportion by volume of distillateD1 required, and the maximum proportion by volume of distillate D3allowed. Solvent S1 must contain at least 50% of distillate D1, andno more than 30% of distillate D3. Solvent S2 must contain at least40% of distillate D1, and no more than 40% of distillate D3. Solvent S3 must contain at least 10% of distillate D1, and no morethan 60% of distillate D3. There are no restrictions on theproportion of distillate D2. The table below specifies theserestrictions and summarizes other relevant information.
Solvent
S1
S2
S3
Cost
Available
Selling price
$5.00
$4.00
$3.00
Minimum Quantity
1,000,000
1,000,000
1,000,000
Min prop of D1
0.5
0.4
0.1
$4.00
1,000,000
Distillate D2
$3.00
1,000,000
Max prop of D3
0.3
0.4
0.6
$2.00
1,000,000
The company aims to maximize profits subject to the specifiedconstraints.
Task 1.1. Formulate the problem as a linearprogramming model. [2 Points]
Decision variables:
Objective Function:
Subject to Constraints:
Task 1.2. Solve the LP model and presentoptimal solutions. [4 Points]
Maximum profit attainable: $…………….
Solvent
S1
S2
S3
Gallons of D1 in
Gallons of D2 in
Gallons of D3 in
Distillate
Available
Used
Surplus
D1
1,000,000
D2
1,000,000
D3
1,000,000
Task 1.3. Sensitivity analysis. [3 Points]
At most how much should the company be willing to pay toincrease the availability of each grade of distillate by 1unit?
Reasoning:
Reasoning:
Reasoning: