10) You are hired as a consulting engineer to a small chemical plant. The plant needs to produce 10,000 liters per day of a liquid with a maximum contaminant concentration of 100 mg/l. There are four suppliers of liquid that can be mixed together to produce the final fluid. Each source sells liquid at a different cost and with different contaminant concentrations. Each supplier has a maximum volume that can be supplied per day. You need to determine how much liquid should be ordered from each supplier to produce 10,000 liters of liquid with no more than 100 mg/l contaminant concentration at the lowest price. The following table summarizes requirements for production (also in Excel).
Use Excel and show all formulas and steps used.
Source 1 |
Source 2 |
Source 3 |
Source 4 |
|
Cost($/L) |
$0.50 |
$0.80 |
$1.20 |
$1.50 |
Max Supply (L/day) |
10,000 |
4,000 |
3,000 |
1,500 |
Concentration (mg/L) |
142 |
105 |
78 |
62 |
Constraints
Constraints |
|
Conc <= |
100 mg/L |
Supply = |
10,000 L |
Let,
x1 = Quantity (in litre) to be ordered from Supplier 1
x2 = Quantity (in litre) to be ordered from Supplier 2
x3 = Quantity (in litre) to be ordered from Supplier 3
x4 = Quantity (in litre) to be ordered from Supplier 4
Objective is to minimize cost so objective function = Min 0.5x1+0.8x2+1.2x3+1.5x4
Subject to,
x1+x2+x3+x4 = 10000 (litres to be ordered)
Max supply available constraints for suppliers
x1 <= 10000
x2 <= 4000
x3 <= 3000
x4 <= 1500
Concentration constraint
(142x1+105x2+78x3+62x4)/(x1+x2+x3+x4) <= 100
or, 42x1+5x2-22x3-38x4 <= 0
x1,x2,x3,x4 >= 0 (Non-negativity constraint)
Solving in excel solver we get,
x1 = Quantity (in litre) to be ordered from Supplier 1 = 2000
x2 = Quantity (in litre) to be ordered from Supplier 2 = 4000
x3 = Quantity (in litre) to be ordered from Supplier 3 = 3000
x4 = Quantity (in litre) to be ordered from Supplier 4 = 1000
Minimized cost = 9300
10) You are hired as a consulting engineer to a small chemical plant. The plant needs...
10) You are hired as a consulting engineer to a small chemical plant. The plant needs to produce 10,000 liters per day of a liquid with a maximum contaminant concentration of 100 mg/l. There are four suppliers of liquid that can be mixed together to produce the final fluid. Each source sells liquid at a different cost and with different contaminant concentrations. Each supplier has a maximum volume that can be supplied per day. You need to determine how much...
The 500-bed Lotta Hart Hospital has a small activated sludge plant to treat its wastewater. The average daily hospital discharge is 1200 L/d per bed, and the average soluble BOD5 after primary settling is 500 mg/L. The aeration tank has effective liquid dimensions of 10.0 m wide x 10.0 m ling x 4.5 m deep. The allowable BOD5 and the suspended solid concentration in the effluent of the secondary treatment unit are 30.0 mg/L and 30.0 mg/L, respectively. Assume that...
please explain steps to solution using excel 9) You are hired as a consulting engineer to a small gasoline refinery. You must determine how many gallons of three different grades of gasoline should be produced to maximize total profit. The gallons produced should not exceed the storage capacity of each grade. Also, there is a maximum of 16,500 eallons of raw oil available to produce the gasoline. The material requirements to produce one gallon of each grade are summarized in...
You are assigned to operate a drinking water treatment plant which has a capacity of 280 ML per day. The source water is from a river that contains a high concentration of dissolved organic carbon (DOC), (13 mg L-1) and has a high colour (60 HU) but where the alkalinity changes seasonally. In summer to winter the alkalinity is high (> 100 mg L-1 as CaCO3) and in spring after snow has melted in the mountains and the water flows...
A wastewater treatment plant that treats wastewater to secondary treatment standards uses a primary sedimentation process followed by conventional activated sludge process composed of covered aeration tanks and secondary clarifiers. You are asked to calculate the different operation parameters to make sure that the system is operated within normal process ranges listed in the reference tables below. Table 5-20 Typical design information for primary sedimentation tanks U.S. customary units Item Unit Range Typical Primary sedimentation tanks followed by secondary treatment...
Based on question 2, how would you go about solving question number 9? Please solve question number 2 and 3 if possible. 2. (10 points) A groundwater in California has the following water quality characteristics. From the analysis shown below, determine the total hardness, carbonate hardness and noncarbonate hardness of the groundwater. Express your answers in units of mg/L as CaCO3 and as meq/L. Constituent Units Concentration or Value 10 90 40 30 10 3.1 Carbon Dioxide (CO2) Calcium (Ca2+)...
10. Write a one-page summary of the attached paper? INTRODUCTION Many problems can develop in activated sludge operation that adversely affect effluent quality with origins in the engineering, hydraulic and microbiological components of the process. The real "heart" of the activated sludge system is the development and maintenance of a mixed microbial culture (activated sludge) that treats wastewater and which can be managed. One definition of a wastewater treatment plant operator is a "bug farmer", one who controls the aeration...
Can you please explain in simple terms the methods of this experiment? I'm having difficulty visualizing and understanding what is being done. I have copied and pasted some of the text from the article. Thank you! Abstract : Obesity, high-fat diets, and subsequent type 2 diabetes (T2DM) are associated with cognitive impairment. Moreover, T2DM increases the risk of Alzheimer's disease (AD) and leads to abnormal elevation of brain beta-amyloid levels, one of the hallmarks of AD. The psychoactive alkaloid caffeine...
Please use own words. Thank you. CASE QUESTIONS AND DISCUSSION > Analyze and discuss the questions listed below in specific detail. A minimum of 4 pages is required; ensure that you answer all questions completely Case Questions Who are the main players (name and position)? What business (es) and industry or industries is the company in? What are the issues and problems facing the company? (Sort them by importance and urgency.) What are the characteristics of the environment in which...
For the preparation and standardization of NaOH with KHP im supposed to boil water for 1hr and 30 min to remove CO2....the problem is that if I don't boil it for that long and (30 min) b/c of not enough time but I put the water I boiled for 1/2 hr aproximately into a NaOH bottle with a CO2 absorber and stored it there for a few days. I would assume that I would have to boil the water again...but...