1. Maximize Z = 2x-y+2z

Subject to: 2x + y 10

x + 2y - 2z 20

y + 2z 5

x, y, z 0

2. A company produces three types of chemicals; A, B and C in two factories; Factory 1 and Factory 2. Factory 1 produces 5 tons of A, 4 tons of B and 1 tone of C per day. Factory 2 can produce 6 tons of A, 3 tons of B and 2 tons of C per day. The daily demand for the chemicals are 250 tones, 150 tones and 60 tons of A, B and C respectively. The daily cost of operations is 50,000 and 70,000 for factory 1 and 2 respectively. Required

(i) Formulate the objective function

(ii) Formulate the constraints

(iii) Hence solve the LP problem using the simplex method