Question

A company produces two product A and B which sales at 5 and 10 shillings respectively. To produce them you required 3 and 2 labor hours of A and B respectively, 2 and 5 machine hours of A and B respectively. 5 litres of blue paint and 4 green paints for B and 3 litre green paint A. In total the company has 400 litres of blue paint, 400 litres of green paint, 400 machine hours and 400 labor hours.



Work out the optimization function and use your answers to match the questions that follow ( Assume x and y represent the number of product A and B produced respectively)

Answer 1

$x=$ quantity A;

$y=$ quantity B;

$3x+2y=400;$

$2x+5y=400;$

$5y <400;y<80;$

$4y+3x=400;$

$2x=400-5y; x=200-2.5y;$

$3×(200-2.5y)+4y=400;$

$200=3.5y; y=57;$

$2x=400-5×57=115; x=115/2;x=57;$

$3×57+2×57=$ 285 labor hours;

$2×57+5×57=399$ machine hours;

$4×57+3×57=399$ green paints;

$5×57=285$ blue paints;

$5×57+10×57=855$ shillings;