ABC Company manufactures both interior and exterior paints from 2 raw materials M1 and M2. The following table gives basic data of problem.
Exterior paint
Interior paint
Availability
N1
6
4
24
N2
1
2
Profit per ton
5
A market survey signifies that every day demand for interior paint cannot surpass that for exterior paint by more than 1 ton. Also maximum routine demand for interior paint is 2 tons. Develop LPP to find out the top product mix of interior and exterior paints that maximizes the daily total gain (profit).
Answer
Assume
x_{1} - number of units of exterior paint
x_{2} - number of units of interior paint
Maximize Z = 5x_{1} + 4x_{2}
Subject to
6x_{1} + 4x_{2 }≤ 24
x_{1} + 2x_{2 }≤ 6
x_{2} - x_{1}≤ 1
x_{2}≤ 2
x_{1}≥0, x_{2} ≥0
b) The highest routine demand for exterior paint is almost 2.5 tons
x_{1}≤ 2.5
c) Routine demand for interior paint is as a minimum 2 tons
x_{2 }≥ 2
d) Routine demand for interior paint is accurately 1 ton more than that for exterior paint.
x_{2 }> x_{1} + 1