I have 4 questions need to be answer No copy paste ! Original work please !I know that you can find answers in chegg but i wany original work and new one ! ChangeJust 2-1 / 2-2 / 2-5 / 2-6 Hand writing too

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Problems

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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) xy = 3, X2 = 1.

(c) x = 3, x2 = 1.5.

(d) x1 = 2, X2 = 1.

(e) Xi = 2, X = -1.

*2-3. For the feasible solution x1 = 1, X2 = 2 of the Reddy Mikks model, determine the un-

used amounts of raw materials M1 and M2.

2-4. Suppose that Reddy Mikks sells its exterior paint to a single wholesaler at a quantity discount.

The profit per ton is $5000 if the contractor buys no more than 5 tons daily and $4300 other-

wise. Express the objective function mathematically. Is the resulting function linear?

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

that x1, x2 > 0.

*(a) -3x + x2 6.

(b) X1 – 2×2 5.

(c) 2x – 3×2 < 12.
(d) x1 - x2 = 0
*(e) x1 + x2 > 0.

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

*(a) Maximize z = x – X2.

(b) Maximize z = -8X1 – 3×2.

(c) Maximize z = -x + 3×2.

*(d) Maximize z = -3×1 + x2.

2-7. Determine the solution space and the optimum solution of the Reddy Mikks model for

each of the following independent changes:

(a) The maximum daily demand for interior paint is 1.9 tons and that for exterior paint

is at most 2.5 tons.

(b) The daily demand for interior paint is at least 2.5 tons.

(c) The daily demand for interior paint is exactly 1 ton higher than that for exterior paint.

(d) The daily availability of raw material Mi is at least 24 tons.

(e) The daily availability of raw material Mi is at least 24 tons, and the daily demand for

interior paint exceeds that for exterior paint by at least 1 ton.

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