Please show the questions step by step through the lingo program PRODUCTION MIX

Question

Please show the questions step by step through the lingo program

PRODUCTION MIX with LINGO

a) Formulate a complete linear programming model in algebraic form that shows the individual constraints and decision
variables for this problem.
b) Using the model obtained in part a and details given in the case study, please fix the highlighted parts of the following
LINGO program so that is produces optimum objective function value of $333680.

The Philbrick Company has two plants on opposite sides of the United States Each of these plants produces the same two products and then sells them to wholesalers within its half of the country. The orders from wholesalers have already been received for the next two months (February and March), where the number of units requested are shown below. (The company is not obligated to completely fill these orders but will do so if it can without decreasing its profits.) Plant 1 Plant 2 Product February 3,600 4,500 March February 6,300 5,400 4,900 5,100 March 4,200 6,000 Each plant has 20 production days available in February and 23 production days available in March to produce and ship these products. Inventories are depleted at the end of January, but each plant has enough inventory capacity to hold 1,000 units total of the two products if an excess amount is produced in February for sale in March In either plant, the cost of holding inventory in this way is S 3 per unit of product 1 and S 4 per unit of product 2. act2 n o Pt % Each plant has the same two production processes, each of which can be used to produce either of the two products. The production cost per unit produced of each t is shown below for each process in each plant. Plant 1 Plant 2 Product Process 1 $ 62 $ 78 Process 2 $ 59 $ 85 Process 1 $ 61 $89 Process 2 $ 65 $ 86 The production rate for each product (number of units produced per day devoted to the product) is given below for each product in each plant. Plant 2 Product Process 1 Process 2 Process 1 Process 2 140 150 100 120 130 160 110 130 2 The net sales revenue (selling price minus normal shipping costs) the company receives when the plant sells the products to its own customers (the wholesalers in its own half of the country) is $ 83 per unit of product 1 and S 112 per unit of product 2. However, it is also possible (and occasionally desirable) for a plant to make a shipment to the other half of the country to help fill the sales of the other plant. When this happens, an extra shipping cost of S 9 per unit of product 1 and $ 7 per unit of product 2 is incured. Management now needs to detemine how much of each product should be produced by each production process in each plant during each month, as well as how much of each plant should sell of each product in each month and how much each plant should ship of each product in each month to the other plant's customers. The objective is to determine which feasible plan would maximize the total profit (total net sales revenue minus the sum of the production costs, inventory costs, and extra shipping costs)

Explanation / Answer

MATCH PARENTHESIS Ctrl+P
Use the MATCH PARENTHESIS command from the Edit menu, click the button, or type Ctrl+P to
find the close parenthesis that corresponds to the open parenthesis you have selected.
In addition to this command, there is one other way to find matching parentheses. LINGO will
highlight matching parentheses in red when the Match Paren option is enabled under the
LINGO|Options command (see below). By placing the cursor immediately after one of the parentheses
of interest, you will notice that the color of the parenthesis changes from black to red. LINGO will
simultaneously display the matching parenthesis in red. These parentheses will remain displayed in red
until you move the cursor to another position.
PASTE FUNCTION
Use the PASTE FUNCTION command from the Edit menu to paste any of LINGO’s built-in functions
at the current insertion point. Choose the category of the LINGO function you want to paste, then
select the function from the cascading menu. LINGO inserts place holders for arguments in the
functions.
SELECT FONT... Ctrl +J
Use the SELECT FONT command from the Edit menu or press Ctrl+J to select a new font in which to
display the currently selected text.
INSERT NEW OBJECT
Use the INSERT NEW OBJECT command from the Edit menu to embed an OLE object into the
LINGO document.
LINKS
Use the LINKS command from the Edit menu to control the links to external objects in your document.
OBJECT PROPERTIES Alt+Enter
Use the OBJECT PROPERTIES command from the Edit menu or press Alt+Enter to specify the
properties of a selected, embedded object
2.2.1 LINGO Menu
SOLUTION… X= Ctrl+W
Use the SOLUTION command from the LINGO menu, click the button, or press Ctrl+W to open the
Solutions dialog box. Here you can specify the way you want a report of the solution currently in
memory to appear. When you click OK, LINGO writes the report to a Report Window.
24 Chapter 2 Solving Math Programs with LINGO
GENERATE… Ctrl+G/Ctrl+Q
Use the DISPLAY MODEL and DON’T DISPLAY MODEL sub-commands from the LINGO Solver |
Generate command or press Ctrl+G or Ctrl+Q, respectively, to create an expanded version of the
current model. The expanded model explicitly lists all the generated constraints and variables in your
model.
If you choose to display the model, LINGO will place a copy of the generated model in a new
window, which you may scroll through to examine, print, or save to disk. If you choose not to display
the model, LINDO will generate the model without displaying it, but will store the generated model for
later use by the appropriate solver.
PICTURE Ctrl+K
Use the PICTURE command from the LINGO menu or press Ctrl+K to display a model in matrix
form. Viewing the model in matrix form can be helpful in identifying special structure in your model.
2.2.2 Windows Menu
COMMAND WINDOW Ctrl +1
Use the COMMAND WINDOW command from the Windows menu or press Ctrl+1 to open LINGO’s
Command Window. The Command Window gives you access to LINGO’s command line interface. In
general, Windows users will not need to make use of the Command Window. It is provided for users
who may want to put together application-specific “products” that make use of LINGO through
Command Window scripts to control the program. Please refer to your help file or user’s manual for
more information on the command line commands.
STATUS WINDOW Ctrl +2
Use the STATUS WINDOW command from the Windows menu or press Ctrl+2 to open LINGO’s
Solver Status window.
2.2.3 Help Menu
HELP TOPICS
Use the HELP TOPICS command from the Help menu, or click on the first question mark button to
open LINGO help to the Contents section. Press the second button (with the arrow) to invoke
context-sensitive help. Once the cursor has changed to the question mark, selecting any command will
take you to help for that command.
REGISTER
Use the REGISTER command from the Help menu to register your version of LINGO online. You will
need a connection to the internet open for this command to work. Enter your personal information in
the dialog box supplied and select the register button. Your information will be sent directly to LINDO
Systems via the Internet.
LINDO Systems is constantly working to make our products faster and easier to use. Registering
your software with LINDO ensures that you will be kept up-to-date on the latest enhancements and
other product news.
Solving Math Problems with LINGO Chapter 2 25
AUTOUPDATE
Use the AUTOUPDATE command from the Help menu to have LINGO automatically check every
time you start the LINGO software whether there is a more recent version of LINGO available for
download on the LINDO Systems website. You will need a connection to the internet open for this
command to work.
ABOUT LINGO…
Use the ABOUT LINGO command from the Help menu to view information about the version of
LINGO you are currently using (e.g., the release number, constraint limit, variable limit, and memory
limit).
2.2.4 Summary
This is not intended to be an exhaustive description of the commands available in the Windows version
of LINGO. Please refer to your help file or user’s manual for a more in-depth analysis.
2.3 Getting Started on a Small Problem
When you start LINGO for Windows, the program opens an <untitled> window for you. For purposes
of introduction, let’s enter the Enginola problem we looked at in the previous chapter directly into this
<untitled> window:
MAX = (20 * A) + (30 * C);
!note that the parentheses aren't needed, because LINGO;
!will do multiplication and division first;
A < 60;
C < 50;
A + 2 * C < 120;
Note, even though the strict inequality, “<”, was entered above, LINGO interprets it as the loose
inequality, “”. The reason is that typical keyboards have only the strict inequalities, < and >. You
may, and in fact are encouraged to, use the two symbols “<=” to emphasize an inequality is of a
less-than-or-equal-to nature. Also, notice comments are preceded by the exclamation mark (!). A
semicolon (;) terminates a comment.
Click on the Solve/“bullseye” button , use the Solve command from the Solve menu, or press
Ctrl+U to solve the model. While solving, LINGO will show the Solver Status Window with
information about the model and the solution process. When it’s done solving, the “State” field should
read “Global Optimum”. Then, click on the “Close” button to close the Solver Status Window:

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