A small iron works manufactures two types of gate. The requirements for each stage of production, along with the limitations on the available labour hours, are given in the following table:

 

 

 

(a)What is  the equations for (i) profit, (ii) total revenue.

 

(b) Write and graph the inequality constraints. Hence, determine graphically the number of each type of gate which should be produced and sold to maximise (i) Profit and (ii) Total revenue.

Gate type Security Ornamental Hours available Stages of production Selling price Welding Finishing 4,5 2,0 900 1,0 2,0 400 (R) 7200 665