The efficiency gains resulting from a just-in-time inventory management system will allow a firm to reduce its level of inventories permanently by $473,000. What is the most the firm should be willing to pay for installing the system

Afinancial institution, the thriftem bank, is in the process of formulating its loan policy for the next quarter. a total of $12 million is allocated for that purpose. being a full-service facility, the bank is obligated to grant loans to different clientele. the following table provides the types of loans, the interest rate charged by the bank, and the possibility of bad debt as estimated from past experience. type of loaninterest rateprobability of bad debtpersonal.140.10car.130.07home.1 20.03farm.125.05commercial.100.02 bad debts are assumed unrecoverable and hence produce no interest revenue either. competition with other financial institutions in the area requires that the bank allocate at least 40% of the total funds to farm and commercial loans. to assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. the bank also has a stated policy specifying that the overall ratio for bad debts on all loans may not exceed .04. formulate this problem as a linear program. define your variables clearly and write all the constraints explaining the significance of each.

Jackson is preparing for his hearing before the federal communications commission (fcc) involving a complaint that was filed against him by the fcc regarding the interruption of radio frequency. the order to "cease and desist" using the radio frequency has had a detrimental impact on his business. once the administrative law judge prepares his or her initial order, jackson has no further options. no, jackson can request that the matter be reviewed by an agency board or commission. yes, once the initial order is presented, it's only a matter of time before the order becomes final.

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.