A firm produces product A and product B. 1 unit of A requires 1 unit of resource 1 and 3 units of resource 2. 1 unit of B requires 4 units of resource 1 and 2 units of resource 2. Daily availability: resource 1 = 20 units, resource 2 = 30 units. Profit per unit: A = ₹50, B = ₹60. Using the simplex method, find the maximum profit.

Step-by-step solution

1. Write LP in standard form: Maximise $Z=50x_1+60x_2$\nsubject to:\n$x_1+4x_{2}le20$\n$3x_1+2x_{2}le30$\n$x_1,x_{2}ge0$
2. Add slack variables $s_1,s_2$: $x_1+4x_2+s_1=20$\n$3x_1+2x_2+s_2=30$
3. Set initial tableau: |BV | $x_1$ | $x_2$ | $s_1$ | $s_2$ | RHS | |----|-----|-----|-----|-----|-----| |$s_1$ | 1 | 4 | 1 | 0 | 20 | |$s_2$ | 3 | 2 | 0 | 1 | 30 | |$Z$ | -50 | -60 | 0 | 0 | 0 |

Concept tested: Simplex method for 2‑var LP

Published 2 September 2026 · How this solution was prepared and checked

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