Suppose a coffee shop wants to serve part of the market (rather than the entire market of all consumers) with two stand-alone locations. Let r > 0 indicate the fraction of customers it plans to sell coffee to either side of each location. The shop earns total profits of (N, n) = N[V - (t/2n) - c] - nF, where N is the number of consumers spaced evenly along the (one-mile) street, n is the number of locations, V is the consumers reservation price, t is the transport cost per unit of distance travelled, c is the cost of supplying a single homogenous cup of coffee, and F is the fixed cost of setting up a new location.

(i) Formally derive the optimal price the coffee shop should charge at each location.

(ii) Use your answer to Q4.(i) above to formally explain how a decrease in the reservation price (V) impacts the optimal price at each location.