Feasible Solution

2-1. For the Reddy Mikks model, construct each of the following constraints, and express it

with a linear left-hand side and a constant right-hand side:

*(a) The daily demand for interior paint exceeds that of exterior paint by at least 1 ton.

(b) The daily usage of raw material M1 in tons is at most 8 and at least 5.

*(c) The demand for exterior paint cannot be less than the demand for interior paint.

(d) The maximum quantity that should be produced of both the interior and the

exterior paint is 15 tons.

*(e) The proportion of exterior paint to the total production of both interior and exterior

paints must not exceed .5.

2-2. Determine the best feasible solution among the following (feasible and infeasible) solutions

of the Reddy Mikks model:

(a) x1 = 1, x2 = 2.

(b) x1 = 3, x2 = 1.

(c) x1 = 3, x2 = 1.5.

(d) x1 = 2, x2 = 1.

(e) x1 = 2, x2 = -1.

2-5. Determine the feasible space for each of the following independent constraints, given

that x1, x2 greater than or equal 0.

*(a) -3×1 + x2 smaller than or equal 6.

(b) x1 – 2×2 greater than or equal 5.

(c) 2×1 – 3×2 smaller than or equal 12.

(d) x1 – x2 smaller than or equal 0.

*(e) -x1 + x2 greater than or equal 0.

2-6. Identify the direction of increase in z in each of the following cases:

*(a) Maximize z = x1 – x2.

(b) Maximize z = -8×1 – 3×2.

(c) Maximize z = -x1 + 3×2.

*(d) Maximize z = -3×1 + x2.