For part (a) it is required to assign x and y and write the objective function.
Let x be the number of gift Basket A purchased and y be the number of gift Basket B purchased.
The objective function of the given information is:
objective function: maxmize z = 12x+15y
For part (b) it is required to write the constraints inequality.
Constraints are:
3x+6y <= 45 rArr x+2y<=16
6x+3y<=36 rArr 2x+y<=12
2x+2y<=18 rArr x+y<=9
For part (c)
It is required to find the intercepts of each inequalities.
x+2y<=16
x/16 + (2y)/16 <= 1 rArr x/6 + y/12 <= 1
intercept of the above inequality is (16,0) and (0,8)
2x+y<=12
(2x)/12+y/12<=1 rArr x/6+y/12<=1
x/16 + (2y)/16 <= 1 rArr x/6 + y/12 <= 1
intercept of the above inequality is (6,0) and (0,12)
x+y<=9
x/9+y/9<=1
intercept of the above inequality is (9,0) and (0,9)