Lagrange Problems: Please show work along with answer
1. Your company is tasked with making time travel machines (T) and Flying saucers. (S). The profit for producing them is given by the following function: F(t,s) = 2000^(1.02) +1500(t^0.5)*s^(0.9) Additionally, you must produce exactly 200 total machines. (obviously, you can’t make negative numbers of either machine.) What number of each will produce your maximum profit?
how many time machines?
2. how many flying saucers?
3. what is the maximal profit?