Question

The country of Freelandia gained independence a few years ago and is mounting a major effort to promote new agricultural development in previously underdeveloped regions. A trucking operator in the town of K has previously been providing only local service. Now that a new major agricultural development program is under way, this operator is considering providing farm-to-market service to carry agricultural and other natural products from their origin in locality M to market at K. The distance is 150 miles (one way), with no intermediate major settlements. After discussions with the local agents of the producers at M, the trucker estimates that the demand function for shipments from M to K is

? = ? + ?₀? − ?₁P

where V is volume in tons per week, Q is frequency of shipments (per week), P is price charged per ton, and a₀, a₁, and Z are parameters. Based upon an average traveling speed of 30 miles per hour, plus a loading or unloading time of 3 hours at each end, he estimates that he can manage at the most one round trip every two days, so Q = 3 per week. He also figures that his costs are related to the mileage he drives per week; his total cost per week is:

?? = ?₀ + ?₁?_?

where m_T = 300Q is the total round-trip mileage driven and b₀and b₁ are parameters. The truck carries 15 tons. He is considering offering an initial frequency of 1 or 2 trips per week at a rate of $25.00 or $30.00 per ton. Assume b₀ = $270, b₁ = $0.50, Z = 25, a₀ = 13, a₁ = 1.

a. For these four combinations of frequency and price, what would be the tonnage carried, the gross revenues, the total cost, and the net revenue?

b. Which of the four options would be preferred by the operator if his objective where to maximize net revenue? To minimize costs? To maximize volume carried? Which option would be preferred by users (shippers)? Can both interests get their first choice simultaneously? If not, why not?

c. For the proposed service the predominant movement is from M to K; the amount of freight to be carried in the reverse direction is negligible. There is a possibility of  picking additional cargo at D to go to M; this would incur a detour of 100 miles additional but could result in an additional load and source of revenue. Would it be profitable for this operator to make the detour? Discuss qualitatively

Answer 1