Mathematics and statistics

Apension fund manager decides to invest a total of at most $40 million in US. Treasury bonds paying 5% annual interest and in mutual funds paying 8% annual interest. He plans to invest at least $5 million in bonds and at least $25 million in mutual funds Bonds have an initial fee of $100 per million dollars, while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than $7000 on fees. How much should be invested in each to maximize annual interest? What is the maximum annual interest? E) The amount that should be invested in Treasury bonds is SD million and the amount that should be invested in mutual funds is 5D million. A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. WarehouseA holds 20 refrigerators already, while warehouse B has 30 on hand. It costs $14 to ship a refrigerator to warehouse A and $12 to ship one to warehouse B. How many refrigerators should be shipped to each warehouse to minimize cost? What is the minimum cost? In order to minimize cost, the manufacturer should ship D refrigerators to warehouseAand D refrigerators to warehouse E. Find the solutions that can be read from the simplex tableau. X1 X2 X3 5 S3 0') ctr-IGOR, 1 8 9 0 2