Problem#3 Develop your operation research formulation and modeling for problem 11.6, part "a", as shown in the below image. Note: there is no need to solve this problem and find the optimal solution 11.6 Amalgamated Engineering makes two kinds of gearbox - manual and automatic. There are four stages in the production of these, with details of times needed and weekly availabilities given below. The company makes a profit of 64 on each manual gearbox sold and 100 on each automatic gearbox. Time available (hours per week) Stage in Time needed manufacture (hours per unit) Manual Automatic Foundry 3 5 Machine shop 5 4 Assembly 2 Testing 1 7,500 10,000 3,500 2,000 (a) Find an optimal solution to the problem. (b) The company can start making a new semiautomatic gearbox that needs 4, 4, 1 and 1 hour respectively in each manufacturing stage, and gives a profit of 80 a unit. Should they make this new gearbox