List of top Mathematics Questions on Linear Programming Problem asked in BITSAT

Minimise \[ Z = \sum_{i=1}^{n} \sum_{j=1}^{m} c_{ij} x_{ij} \]

Subject to:
\[ \sum_{i=1}^{n} x_{ij} = b_j, \quad j = 1, 2, \dots, m \]
\[ \sum_{j=1}^{m} x_{ij} = b_i, \quad i = 1, 2, \dots, n \]

This is a linear programming problem (LPP) with number of constraints:

The maximum value of \(z = 3x + 2y\) subject to \(x + 2y \ge 2\), \(x + 2y \le 8\), \(y \ge 0\) is

Minimise \( Z=\sum_{i=1}^{n}\sum_{j=1}^{m} c_{ij}x_{ij} \) subject to \[ \sum_{i=1}^{m} x_{ij}=b_j,\; j=1,2,\ldots,n, \] \[ \sum_{j=1}^{n} x_{ij}=b_i,\; i=1,2,\ldots,m. \] This is an LPP with number of constraints equal to

Prabhat wants to invest the total amount of ₹15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least ₹2,000 in saving certificates and ₹2,500 in national saving bonds. The interest rate is 8% on saving certificates and 10% on national saving bonds per annum. He invests \( x \) in saving certificate and \( y \) in national saving bonds. Then the objective function for this problem is:

A wholesale merchant wants to start the business of cereal with ₹24000. Wheat is ₹400 per quintal and rice is ₹600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit ₹25 per quintal on wheat and ₹40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then maximum profit is the objective function