PLEASE include your Excel file. A photocopy machine company produces three types

Question

PLEASE include your Excel file.

A photocopy machine company produces three types of laser printers the Print Jet, the Print Desk, and the Print Pro. The resource requirements and profit for each model are shown in the table below. Market demands indicate that they can only sell a total of 700 printers - combination of all models - in a month (because of limited resources - there is a possibility that they will not be able to produce 700 printers). The company wants to ensure that the Print Jet constitutes at least 40% of the total production. The Print Pro and Print Desk together constitute at least 20% of the total production. The company is profit oriented and looking to determine how many of each printer should be produced. The company is looking determine how much of each product should be produced next month, so the number of each product should be an integer. Formulate this as an LP problem and solve in Excel. What is the total profit for your product mix strategy? How many of each product should be produced? It turns out that the production manager has a part-time worker who can work 20 hours next month, what department would you assign him/her to? Why? Be sure to paste your Excel solution into this answer box for full/partial credit.

Explanation / Answer

A photocopy machine company produces three types of laser printers
which are given below:-

Let number of print jet = x
number of print desk = y
& number of print pro = z

To maximize profits are:- 75x + 93y + 102z

Here is the given value:-
Total assembly time is 1900   
& total testing time = 2500

subject to the constraints:-
4.0x + 3.7y + 4.1z <= 1900 {Total assembly time is 1900}
1.8x + 2.2y + 1.2z <= 2500 {total testing time is 2500 }
According to question

x >= 0.4(x+y+z)
0.6x-0.4y-0.4z >= 0
or 0.4y+0.4z-0.6x <=0 -------eq(1)
&
y+z >= 0.2(x+y+z)
0.8y+0.8z-0.2x >= 0
or 0.2x-0.8y-0.8z <=0 --------eq(2)

and x>=0, y>=0, z>=0 --------eq(3)

Solving this equation and we get:-

x=280
y= 140
z= 140

Total profit = 21000 + 13020 + 14280 = 48300

Total products should be produced = 280+140+140 = 560

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