A carpenter makes two types of chairs for a school. To make type A chairs it takes 6 man hours and 4 man hours for type B. The cost of material for type A is sh 120 and that of type B is sh100. The profit on type A is sh80 and that of type B is sh60. The carpenter has to abide to the following conditions:
i) a contract to supply 15 of type A and 10 of type B per week has to be fulfilled
ii) only 300 man hours are available a week
iii) total weekly cost of material for all chairs should not exceed sh 6000 if type A and B chairs were x and y respectively
a) Write down the inequalities satisfying these conditions
b) What values of x and y will give maximum profit