12. A company produces three products \( P, Q \) and \( R \) whose prices per unit are 3,5 and 4 respectively. One unit of product \( P \) requires 2 units of \( m_{1} \) and 3 units of \( m_{2} \). One unit of product \( Q \) requires 2 units of \( m_{2} \) and 5 units of \( m_{3} \) and one unit of product \( R \) requires 3 units of \( m_{1}, 2 \) units of \( m_{2} \) and 4 units of \( m_{3} \). The company has 8 units of material \( m_{1}, 10 \) units of material \( m_{2} \) and 15 units of material \( m_{3} \) available to it.
(i) Formulate the problem mathematically.
(ii) Use simplex method to find how many units of each product should be produced to maximizc revenue ?
[Delhi Univ. B.Com. (H) 1985]