4. There is a city that stretches from point A to point B, one mile long, and citizens live uniformly spread along this line. A B Walking each mile (to buy a good) entails a travel cost of c. So, if a citizen lives d miles from a store, she has to incur a travel cost of cd to buy goods from that store. There is a duopoly of two firms, 1 and 2, selling apples, located at the two ends of the city, that is, at A and B, respectively. Each firm i's has to choose a price p. Each citizen buys exactly one apple and goes to the store where the price plus the travel cost is less. (a) Consider a citizen who lives at a distance d from A (or 1-d from B). Write down an inequality involving p,, p., c and d, such that the citizen buys from firm 1 if and only if that inequality is satisfied