Mathematical Model Is an Abstract of Any Mathematical Real Time Situation

Note: Objective is to develop a mathematical model. Then check the math principals that is resembles. Solve the case and check the solution.

Mathematical model is an abstract of any mathematical real time situation.

For this Problem:-

Objective of the situation: Maximizing profit.

Decision variables: How many Kgs of X1 produce and X2 to produce

Constraint: Process time (T1<= 400, T2<= 600)   T1= roasting section, T2= Grinding/packing section

(Total Profit)Max Z=40X1 +60X2

20X1+40X2<=400

40X1+30X2<= 600

X1, X2>= 0

Assumptions made to develop the model: Same time for each kg (check names from book), proportionality, linearity,

No probability cases present here, only we will deal with specific nos.

Steps:-

Find Objectives

Select Decision variable

Check Constraints

Get solution

Coffee Product Mix Decision: Mother’s Recipe, a popular coffee manufacturer produces two flavors of coffee powders- Cappuccino and Espresso. The firm uses two operations – (1) Roasting and (2) Grinding and Packing. To produce one kilogram of Cappuccino, 20 minutes of Roasting section time and 40 minutes of Grinding/Packaging section time is needed, while one kilogram of Espresso requires 40 minutes of roasting and 30 minutes of grinding/packaging section. The time available in the roasting section is 400 minutes per day and 600 minutes are available with grinding/packaging section. Since, Mother’s Recipe enjoys good reputation in the city, whatever they manufacture can be sold on the day itself. One kilogram of Cappuccino fetches profit of Rs. 40 whereas one kilogram of Espresso gives Rs. 60. Develop a linear programming problem for Mother’s Recipe.

20X1+40X2<=400

X1=0, X2=10 (0,10)

X2=0,X1=20

40X1+30X2<= 600

X1=0,

X2=0,X1=15

Furniture Manufacturing

A furniture company manufactures desks and chairs.  There are four departments namely carpentry, upholstery, painting and varnishing with capacities as given below:

        Assuming that raw materials are available in adequate quantities and the manufacturer wishes to know how many desks and chairs he should produce.  He enjoys a good market share.  The contribution from a desk is Rs.40/- and that from a chair is Rs.25/-