Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: Potential Locations for Substations Areas Covered A 1, 5, 7 B 1, 2, 5, 7 C 1, 3, 5 D 2, 4, 5 E 3, 4, 6 F 4, 5, 6 G 1, 5, 6, 7 Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas.

Subway, with more than 27,000 outlets in the U.S., is planning for a new restaurant in Buffalo, New York. Three locations are being considered. The following table gives the factors for each site. Factor Space Costs Traffic density Neighborhood income Zoning laws Weight 0.30 0.25 0.20 0.15 0.10 Maitland 60 40 55 50 75 Baptist Church 70 85 85 75 20 Northside Mall 75 25 60 45 90 a) Based on the given information, the best location in Buffalo for Subway to open the new restaurant is , with a total weighted score of (Enter your response rounded to two decimal places.) b) If the weights for Space and Traffic density are reversed, the best location in Buffalo for Subway to open the new restaurant will be weighted score of (Enter your response rounded to two decimal places.) with a total

please solve all parts within 30 minutes.

A council has a brown-field sites designated for social housing. After allowing for roads and parks it has an area of 150000 m² for social housing. The housing association intends to build a mixture of flats, two-bedroom houses, three-bedroom houses, and shops (which include a living space) on this site. The housing association wishes to maximise the number of people that can be housed but has strict housing requirements: • there must be at least twice as many two-bedroom houses as three-bedroom houses; • at least 10% of the total housing units excluding shops (i.e. flats and houses) must be flats; • buildings containing the flats (i.e a "block") must have two storeys and every flat must have the same floor space; • shops must be provided at a rate of at least one per 1500 inhabitants. The average number of inhabitants per housing unit and the ground floor area of each are given in the following table. Housing type Flat Two-bedroom house Three-bedroom house Shop Average number of…

6 see pictures to solve

Ross​ Hopkins, president of Hopkins​ Hospitality, has developed the​ tasks, durations, and predecessor relationships in the following table for building new motels.  ​ Activity    a    m    b    Immediate Predecessor(s)    Activity    a    m    b    Immediate Predecessor(s)A    6    8    12    -    G    2    3    4    C, EB    1    9    24    A    H    2    2    2    FC    8    14    16    A    I    7    7    7    FD    4    7    10    A    J    6    7    12    D, G, HE    1    2    4    B    K    1    1    4    I, JF    6    9    20    C, E                     a) The expected​ (estimated) time for activity C is 13.33weeks. ​(Round your response to two decimal​ places.)   ​b) The variance for activity C is 1.78weeks. ​(Round your response to two decimal​ places.)   ​c) Based on the calculation of the estimated​ times, the critical path is A - C - F - H - J - K   . ​d) The estimated time for the critical path is [ ? ] enter your response here weeks. ​(Round your response to two…