Problem 3. Solve it by the simplex method, following the steps. You should start from the basis given by the slack variables. max 50ci + 40:12 s.t. 311 + 2:12 0. 9 Step 1. Write the LP in standard form. Step 2. Identify and write down c, b and A. Step 3. For the basis consisting of the slack variables, identify and write down B, 2B, CB and AB. Also identify and write down N, and c; and A for each j EN. Step 4. Calculate Ag+, Ag+b and AgA for each jeN. Now write down the special form of the LP equations, IB = (AB)-16 - (AB)-Aix;. JEN Verify that the current basis is indeed feasible. Step 5. Calculate Agb and c; -CAR-A for each je N. Now write down the special form of the LP objective, CAB+6+ E (c; - CABA')?;. JEN Step 6. Identify the entering variable by Bland's rule. Step 7. Identify the leaving variable (carry out the ratio test) by Bland's rule. Hence determine the new basis. Step 8. Repeat steps 3 through 7 until you determine that the current basis is optimal. Write down the optimal solution of the LP and state its optimal value