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The country of Freelandia gained independence a few years agoand is mounting a major effort to promote new agriculturaldevelopment in previously underdeveloped regions. A truckingoperator in the town of K has previously been providing only localservice. Now that a new major agricultural development program isunder way, this operator is considering providing farm-to-marketservice to carry agricultural and other natural products from theirorigin in locality M to market at K. The distance is 150 miles (oneway), with no intermediate major settlements. After discussionswith the local agents of the producers at M, the trucker estimatesthat 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 averagetraveling speed of 30 miles per hour, plus a loading or unloadingtime of 3 hours at each end, he estimates that he can manage at themost one round trip every two days, so Q = 3 per week. He alsofigures that his costs are related to the mileage he drives perweek; his total cost per week is:

?? = ?₀ + ?₁?_?

where m_T = 300Q is the total round-trip mileagedriven and b₀and b₁ are parameters. The truckcarries 15 tons. He is considering offering an initial frequency of1 or 2 trips per week at a rate of $25.00 or $30.00 per ton. Assumeb₀ = $270, b₁ = $0.50, Z = 25, a₀= 13, a₁ = 1.

a. For these four combinations of frequency and price, whatwould 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 operatorif his objective where to maximize net revenue? To minimize costs?To maximize volume carried? Which option would be preferred byusers (shippers)? Can both interests get their first choicesimultaneously? If not, why not?

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