(CLO1(C3) Solve linear programming problems using graphical and simplex methods; and CLO2 (C3) Solve transportation problems using suitable transportation and network model)

A company sells bran and chia muffins that are processed using two difference processors. Processor A can only be operated for 52 hours a week, while processor B can only be operated for 36 hours a week. The bran muffin requires two hours in processor A and two hours in processor B, while the chia muffin requires two hours in processor A and one hours in processor B. Profits from the bran and chia muffins are RM 8 and RM 10 respectively.

1. Use the graphical method to determine the maximum number of these products that needs to be produced weekly for maximum profit (the point of intersection must be shown correctly on a scaled graph paper and verified using solutions from simultaneous equations).
2. Use the simplex method to find the same solution
3. The company owns four bakeries and four cafes. Table 1a shows the location, monthly supply and demand between the bakeries and the cafes. Table 1b provides the transportation cost from the bakeries to the cafes. Determine the minimum cost bearable by applying both the North West Corner Method and the Vogels Approximation Method and compare.

Table 1a / Jadual1a

Bakery Location/ Lokasi Bakeri	Monthly Supply/ Bekalan Bulanan	Cafe/ Kafe	Monthly Demand/ Permintaan Bulanan
Petaling Jaya	150	Fennel	180
Wangsa Maju	180	Lemonie	160
Ampang	100	Poppy	170
Puchong	220	Reverie	140

Table 1b / Jadual1b

Bakery Location/ Lokasi Bakeri	Fennel (RM)	Lemonie (RM)	Poppy (RM)	Reverie (RM)
Petaling Jaya	4	4	5	5
Wangsa Maju	4	5	6	6
Ampang Jaya	6	7	6	7
Puchong	8	7	6	7