Laboratory 10 Problem 1 Use both the graphical and simplex m

Laboratory 10 Problem 1 Use both the graphical and simplex methods to solve: A potter is making cups and plates. It takes her 12 minutes to make a cup and 6 minutes to make a plate. Each cup uses 375 grams of clay and each plate uses 500 grams of clay. She has 40 hours available for making the cups and plates and has 125 Kg of clay in hand. She makes a profit of $6 on each cup and $4.50 on each plate. How many cups and how many plates should she make in order to maximize her profit?

Solution

to get x= 3.33 y =0 or x=0 y=6.67.the intersection of two lines is not possible as x,y >0

As x and y are integers

(3,0) and (0,6) are feasible solutions

Profit for (3,0) = 18 and profit for (0,6) =27

Hence 6 plates only can be made to get max profit.

	X	Y
	Cups	Plates
Time	12 min	6 min
Clay	375 gm	500 gm
Hours ava.	12x+6y<=	40
Clay avail	375x+500y<=125000
Profit	6	4.5
Objective is to maximise profit
P = 6x+4.5y
Solve the inequalities