For the following linear program maximize ₁+8x2+3x3 subject to 21 +8x2+2x3≤4, 2x+4x2+3x3 ≤ 4, 1+22+3≤1, x1, x2, x30 determine whether x = (0,1,0) is an optimal solution using the principle of com- plementary slackness.

Q5) Solve the following linear programming by using simplex method: Max Z=4X1 + 5X2 Subject to: X1 + X2 < 10 3X1 + 7X2 < 42 X1, X2 20

A fruit basket vendor purchases apples and oranges. The number of apples must be at least 2 times the number of oranges but no more than 3 times the number of oranges. The vendor wants to buy at least 8 of each kind of fruit but no more than a total of 30. Some order combinations of fruit expressed as (# of oranges, # of apples) are shown below. Determine if the order combination meets the constraints or not. (7, 21) [ Select] (8, 17) [ Select] (8, 21) [ Select] (8, 23) [ Select] (9, 17) [ Select] (9, 21) [ Select ] (10, 20) [ Select] > > > > > >

Use Lagrange multipliers to find three positive numbers whose sum is 110 and whose product is maximum. (Enter your answers as a comma-separated list.)