wg lime is reduced to 48 hours/week? Problem 3 [300] Dr. Jaz Optimax has recently been named the Minister of World Trade (MWT) for a new nation called WakandaMax. In connection with this position, she has decided that the welfare of the country could best be served by maximizing the net dollar value of the country's exports for the coming year. (The net dollar value of exports is defined as exports less the cost of all materials imported by the country) WakandaMax has traditionally made three products for export: steel, heavy machinery, and trucks. For the coming year. Dr. Optimax believes that the country could sell all it that it produces of the three products at existing world market prices of $900/unit for steel $2.500/unit for machinery $1,650/unit for trucks In order to produce one unit of steel with the country's existing technology, the following are needed: 0.05 units of machinery 0.08 units of tracks 2.0 units of ore purchased on the world market for S100/unit . . Other imported materials costing $100 0.5 person-years of labor The steel mills of WakandaMax have a maximum usable capacity of 300,000 units per year. To produce one unit of machinery requires the following: 0.75 units of steel 0.12 units of trucks 5 person-years of labor $150 of material that must be imported for each unit of machinery produced The practical capacity of the country's machinery plants is 50,000 units per year. In order to produce one unit of trucks, the following are required: 1.0 unit of steel 0.10 units of machinery 3 person-years of labor $500 of material that must be imported for each unit of trucks produced Existing truck capacity is 550,000 units per year. The total labor force available for production of steel, machinery and trucks is 1,200,000 person-unit per year. Provide concise and clear short answers to the following questions using the LINDO model and the LINDO solution (output) provided on the next page. Please show all work and fully substantiate your answers. a) (30) What is the optimal production and export mix for WakandaMax? What would be the net dollar value of exports under this plan? b) (30) There is a chance that Dr. Optimax may have $650,000 to spend on expanding capacity. If this investment can buy 450 units of truck capacity or 1,100 units of machine capacity, or 310 units of steel capacity, what would the best investment be? Why? c) 140) If the world market price of the imported materials needed to produce one unit of trucks were to increase by $350, what would be the optimal export mix for WakandaMax, and what would be the dollar value of its net exports d) (50) The Minister of Defense recently told Dr. Optimax that she wants to stockpile (add to inventory) 7,000 units of steel during the coming year. How will this change the model formulation, and what will be the new value of net dollar exports? e) [50] Union members are threatening to go on strike for one year. If they do, the total labor-power (person- units) available will drop to 750,000. Dr. Optimax is concerned that this will adversely affect the net dollar value of exports. Will it, and if so, by how much? 150] If the selling price of steel on the world market fell from $900 to $880, would it be desirable to start exporting trucks? How can you tell? g) [50] Suppose that Dr. Optimax could buy 12 additional units of steel-making capacity and if the total price for these additional units is $3,500, should she purchase them? Please explain your reasoning fully. LINDO MODEL Title WakandaMax Sensitivity Analysis for Dr. Jaz Optimax Maximize Profit) 989 exsteel + 2589 exmach + 1650 extruk - 380 totsteel - 150 totmach-580 tottruk SUBJECT TO Steel) - exsteel + totsteel - 0.75 totmach - tottruk - Machnry) - exmach - 0.65 totsteel + totmach - 0.10 tottruk - Trucks) -extruk - 0.08 totsteel - 0.12 totmach + tottuk - AVSteel) totsteel
