Amanufacturer is producing two types of shoes, types a and b. type a cost $4 to produce and takes one hour. type b costs $5 dollars to produce and takes 12 1 2 hour. type a yields a profit of $10 and type b yields a profit of $12. the manufacturer has $40 and 7 production hours available. how many of each type of shoe should the manufacturer produce to maximize profit?