會MATLAB的大大幫忙解題，感恩

mike1207

OPTIMIZATION  METHODS  MID-TERM  EXAMINATION

1.將下列問題，列出其目標函數及限制條件

  a. Transportation problem ( minimize transportation cost)
    m plants, n warehouse
    s i  supply of  ith plant , i=1……..m

    d j demand of jth warehouse, j=1….n

    c ij cost of transportation i→j

    x ij number of unite to send i→j

b. Manufacturing (maximize profit)
   products, m raw materials

   c  j.:profit of product j

    b i  :available units of material i

    a i j :＃units of material  i  product j needs in order to be proced

  x j :amount product j produced

c. Scheduling (Goal: hire minimum number of nurses)
   Hospital wants to make weekly nightshift of its nurses

   d  j : demand for nurses each day, j =1,2…,7

   Every nurse works 5days in a row

   X j :＃nurses starting their work on day  j