You have been hired to assist the DKFF in determining how to 'optimally' distribute up to $1,250.000 (1250K) in charitable giving to a set ofS possible 'causes' (shown as Cause A through H) devoted to enhancing rural health in America. CAUSE A B C D E F G H MAX 3?5 250 450 300 600 350 200 260 Category M S L 5 L M S M Value 6.5 5.2 4.7 2.1 4.8 6.9 5.5 4 Responsibilit~,-r 4 3.2 4.8 2.8 4.2 3.4 3.8 5 Note that you can distribute less than the 1750K. Each Cause has attributes related to charitable giving and the DKFF algorithm for contribution management. MAX = maximum amount (in 000's) that can be given to that Cause. Category = Is it a small (S). medium (M) or large (L) organization. Value = The assessed socio-economic value for each 5 invested. Responsibility = the DKFF determined assessment {A scale of 1-5) on the legitimacy of the organization and its ratio of how much money goes to administration vs. the charitable cause itself. Used in a weighted average constraint. Create an LP model (forcing integer solutions) that finds the optimal way to invest up to [but possible less than) S 1 250K in these 8 Causes. subject to the following restrictions. and maximizing the overall Value for the investments. a) Make sure no more than the IMAX amount is allocated to each Cause as specied above. b) h-Iake sure the model limits the total investment to 1250K. It can be less than that. c) \"he total amount of investment in each of the three categories must be at least 30% of the overall amount invested. Note that we do not know ahead of time the total amount invested. d) \"he average responsibility measure for all investments must be greater than or equal to 4.25