4. (20 points) Suppose you are consulting for a company which plans to build gas stations along a road. Along the road there are major intersections every 2 miles, which are potentially good locations for new gas stations. The gas stations at different intersections have different estimated profits. The company has decided not to build gas stations at adjacent major intersections, i.e., two gas stations will have to be at least 4 miles away from each other. Given the estimated annual profit for having a new gas station at each intersection, you are asked to provide an optimal plan that will result in the highest estimated total profit. (Hint: this can be considered as a simpler version of the restaurant lotion problem.) a. Let F(i) be the estimated total profit of the optimal plan that considers only intersections 1 to i. Write down the recurrence function for computing F(i) b. Show how to use the recurrence function and dynamic programming to find the optimal plan given the estimated profits below. 213141516171819|10 | 11 | 12 | 13 | 14 | 15