Statistics

A pension fund manager decides to invest a total of at most $25 million in US. Treasury bonds paying 3% annual interest and in mutual funds paying 5% annual interest. He plans to invest at least $5 million in bonds and at least $10 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 $4000 on fees. How much should be invested in each to maximize annual interest? What is the maximum annual interest? (3 The amount that should be invested in Treasury bonds is SD million and the amount that should be invested in mutual funds is $11 million. Acompany is considering two insurance plans with coverage and Policy A Policy B (L premiums shown in the table. (For example. this means that $50 buys \"fen-heft $10,000 $15,000 one unit of plan A, consisting of$10.000 re and theft insurance and . . . $180,000 of liability insurance.)Answer parts (a) and (b). \"ab"\"y \"30'0\"\" \"20'0"" Premium $50 $40 E) (a) The company needs at least $300000 re and theft insurance and at least $3.600,000 liability from these plans. How many units should be purchased from each plan to minimize the cost of the premiums? What is the minimum premium? The company should purchase [:I units of Policy A and El units of Policy B, for a premium of SD. (b) Suppose the premium for policyA is reduced to $25. Now how many units should be purchased from each plan to minimize the cost of the premiums? What is the minimum premium? Amanufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses Each warehouse holds a maximum of 100 refrigerators. Warehouse Aholds 25 refrigerators already, while warehouse B has 30 on hand. It costs $12 to ship a refrigerator to warehouse A and $15 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 warehouseA and D refrigerators to warehouse B