A group of students plan to sell x hamburgers and y chicken burgers at a soccer match. They have meat for at most 300 hamburgers and at most 400 chicken burgers. Each burger of both types is sold in a packet. There are 500 packets available. The demand is likely to be such that the number of chicken burgers sold is at least half the number of hamburgers sold.
(a) Write the constraint inequalities.
(b) A profit of $2 is made on each hamburger sold and $1 on each chicken burger sold. Write the equation which represents the total profit, P, in terms of x and y.
(c) The objective is to maximize profit. Draw a search line on the graph paper by indicating it as a dotted line in its optimum position.
(d) How many, of each type of burger, should be sold to maximize profit?