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This paper is on the application of Linear Programming Problem on Niger Mills Company PLC Calabar, Cross River State, Nigeria and intended to determine the quantity of Golden Penny flour (50kg bags), Golden Penny semovita (10kg bags) and Wheat offals (50kg bags) that Niger Mills Company PLC Calabar should produce in a day in order to maximize profit, given the constraints posed in the production process. A problem of this nature was identified as a linear programming problem, formulated in mathematical terms and solved by the available computer soft wares (Excel Solver and TORA) for solving Linear Programming problems. The solution obtained reveals that 576 (50kg) bags of flour, non presently for Semovita and wheat offals should be produced daily, in order for the company to achieve a maximum daily profit of N161,280.00. Sensitivity analysis was also conducted to review the following; changing the objective function coefficient for a variable, forcing a variable which is currently zero to be non-zero, and changing the right-hand side of a constraint. The sensitivity analysis revealed that for Semovita (variable X2), the objective function needs to change by 60.00000091 (increase since we are maximizing) before it becomes non-zero. In order words, referring back to our original situation in this research work, the profit per unit on semovita would need to increase by 60.00000091 before it would be profitable to produce any of semovita products. Similarly, the profit per unit on W/offals would need to increase by 45.0000002 before it would be profitable to produce any of W/offals products.