Question: 1) Consider the following all-integer linear program. Max 1 x 1 + 1 x 2 s.t. 4 x 1 + 7 x 2 31 1

1) Consider the following all-integer linear program.

Max	1x₁	+	1x₂
s.t.
	4x₁	+	7x₂	31
	1x₁	+	6x₂	24
	2x₁	+	1x₂	13
x₁, x₂ 0 and integer

1) Consider the following all-integer linear

Consider the following all-integer linear program. Maxs.t.x1,x21x1+1x24x1+7x2311x1+6x2242x1+1x2130andinteger (b) Solve the LP Relaxation of this problem. at (x1,x2)=( (c) Find the optimal integer solution. x4= the number of 4cyl inder connecting rods produced next week xG= the number of 6cylinder connecting rods produced next week 54=1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise s6=1 if the production line is set up to produce the 6cy inder connecting rods; 0 if otherwise (c) Write a third constraint that, taken with the constraints from parts (a) and (b), limits the production of connecting rods for next week. (d) Write an objective function for minimizing the cost of production for next week. Min

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