I need help with number 1

For each of the following problems give: A. The function that represents the quantity to be optimized. This includes specifying the parameters. E.g. F(I, J): this represents the maximum number of coins that the robot can pick up from a rectangle of size IxJ made up of the first I rows and first J columns.. B. The recurrence formula: the formula that specifies the recurrence relation that represents the relationship between larger problems and smaller problems. E.g. for the robot problem F(l, J):- max {F(l, J), F(I, J)} + 6 i j where 5 i, j - 1 if there is a coin in the i j square and 0 if not C. The base cases: E.g. F(0, J)- F(I, 0) _ 0 for all I from 0 to N and all J from 0 to M D. The final solution: E.g. F(N, M) if the original problem is stated as an N times M board E. The pseudo code for the iterative algorithm to fill in a table that would be used for a bottom up dynamic programming solution 1. Given an unlimited supply of coins of denominations 1 -d_1 0 and i - 1; 2;:::; n. Any two restaurants must be at least k miles apart, where k is a positive integer. Give a dynamic programming algorithm to compute the maximum expected total profit subject to the given constraints. 4. You are going on a long trip. You start on the road at mile post 0. Along the way there are n hotels, at mile posts a_1