Please Use Excel! You are hired as a consulting engineer to a small chemical pla
ID: 3147839 • Letter: P
Question
Please Use Excel!
You are hired as a consulting engineer to a small chemical plant. You need to determine how many gallons of fluids A, B, C and D should be produced each day to maximize the profit. Fractional gallons to 1 decimal place are acceptable. The quantity of each product cannot exceed the maximum possible dailt storage of each product. The fluids are produced from a raw oil which has a daily availability of 350 gallons. The fluids must be processed in three separate departments. Each department has a maximum number of hours available. The following tables summarize the data to produce 1 gallon of fluid for each department.
Hours
Hours
Hours
Gallons
Maximum
Needed
Needed
Needed
Selling
Raw
Gallons
Dept 1
Dept 2
Dept 3
Cost
Price
Needed
Storage
Fluid A
1
1.25
0.75
$4.35
$5.00
1.3
50
Fluid B
0.7
1
1.1
$3.50
$4.25
1.2
90
Fluid C
1.1
0.75
1
$4.00
$4.85
1.35
80
Fluid D
1.3
1.1
1.2
$4.25
$5.75
1.42
75
Max Gallons of Raw Oil
350
Avail Hrs Dept 1
250
Avail Hrs Dept 2
225
Avail Hrs Dept 3
250
Hours
Hours
Hours
Gallons
Maximum
Needed
Needed
Needed
Selling
Raw
Gallons
Dept 1
Dept 2
Dept 3
Cost
Price
Needed
Storage
Fluid A
1
1.25
0.75
$4.35
$5.00
1.3
50
Fluid B
0.7
1
1.1
$3.50
$4.25
1.2
90
Fluid C
1.1
0.75
1
$4.00
$4.85
1.35
80
Fluid D
1.3
1.1
1.2
$4.25
$5.75
1.42
75
Homework 9 Problem 6 You are hired as a consulting engineer to a small chemical plant. You need to determine how many gallons of fluids A, B, C and D should be produced each day to maximize the profit. Fractional gallons to 1 decimal place are acceptable. The quantity of each product cannot exceed the maximum possible dailt storage of each product. The fluids are produced from a raw oil which has a daily availability of 350 gallons. The fluids must be processed in three separate departments. Each department has a maximum number of hours available. The following tables summarize the data to produce 1 gallon of fluid for each department. Hours GallonsMaximum Hours Needed Needed Needed Dept 1 Dept 2Dept3 1.25 Hours Selling Raw Gallons NeededStorage Cost $4.35$5.00 $3.50$4.25 4.00$4.85 $4.25 $5.75 Price Fluid A Fluid B Fluid C Fluid D 1.3 1.2 1.35 1.42 50 90 80 75 0.7 0.75 1.3 1.1 1.2 Max Gallons of Raw Ol Avail Hrs Dept 1 Avail Hrs Dept 2 Avail Hrs Dept3 350 250 225 250Explanation / Answer
the optimization says put 192.3 gallons of Fluid D and rest all 0.
LPP
1. variable - optimal quantity of al lthe fluid types - A, B, C, D
constraints
1. Dep1 hours = A + 0.7B + 1.1C + 1.3D <= 250
2. Dep2 hours = 1.25A + 1B + 0.75C + 1.1D <= 225
3. Dep3 hours = 0.75A + 1.1B + C + 1.2D <= 250
4. A <= 50, B <= 90, C <= 80, D <= 75 (storage constraint)
5. 1.3A+1.2B+1.35C+1.42D <= 350 (raw oil constraint)
Objective
Maximize the profit = 0.65A + 0.75B + 0.85C + 1.5D
Fluid quantity Hours needs Raw Gallons constraint Type optimal Dept 1 Dept 2 Dept 3 Needed Storage storage Cost Selling price profit Fluid A 0 1 1.25 0.75 1.3 50 50 $4.35 $5.00 0.65 Fluid B 0 0.7 1 1.1 1.2 90 90 $3.50 $4.25 0.75 Fluid C 0 1.1 0.75 1 1.35 80 80 $4.00 $4.85 0.85 Fluid D 192.3 1.3 1.1 1.2 1.42 75 0 $4.25 $5.75 1.5 limit 250 225 250 350 total 250 211.5385 230.7692 273.07692 288.4615 Constraints 0 13.46154 19.23077 76.923076Related Questions
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