Jean-Pierre Leveque has recently been named the Minister of International Trade for the new…

Jean-Pierre Leveque has recently been named the Minister of International Trade for the new nation of New France. In connection with this position, he has decided that the welfare of the country (and his performance) 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.)

 The area that now constitutes New France has traditionally made three products for export: steel, heavy machinery, and trucks. For the coming year, Jean-Pierre feels that they could sell all that they could produce of these three items at existing world market prices of $900/unit for steel, $2500/unit for machinery, and $3000/unit for trucks

 In order to produce one unit of steel with the country’s existing technology, it takes 0.05 units of machinery, 0.08 units of trucks, two units of ore purchased on the world market for $100/unit, and other imported materials costing $100. In addition, it takes .5 man-years of labor to produce each unit of steel. The steel mills of New France have a maximum usable capacity of 300,000 units/year.

To produce one unit of machinery requires .75 units of steel, 0.12 units of trucks, and 5 man-years of labor. In addition, $150 of materials must be imported for each unit of machinery produced. The practical capacity of the country’s machinery plants is 50,000 units/year.

 In order to produce one unit of trucks, it takes one unit of steel, 0.10 units of machinery, three man-years of labor, and $500 worth of imported materials. Existing truck capacity is 550,000 units/year. The total manpower available for production of steel, machinery, and trucks is 1,200,000 men/year.

To help Jean-Pierre in his planning, he had one of his staff formulate the model shown in Fig. and solved in Fig. Referring to these two exhibits, he has asked you to help him with the following questions:

a) What is the optimal production and export mix for New France, based on Fig.? What would be the net dollar value of exports under this plan?

 b) What do the first three constraint equations (STEEL, MACHIN, and TRUCK) represent? Why are they equality constraints?

c) The optimal solution suggests that New France produce 50,000 units of machinery. How are those units to be utilized during the year?

d) What would happen to the value of net exports if the world market price of steel increased to $1225/unit and the country chose to export one unit of steel?

Jean-Pierre Leveque has recently been named the Minister of International Trade for the new nation...-1

 

e) If New France wants to identify other products it can profitably produce and export, what characteristics should those products have?

f) There is a chance that Jean-Pierre may have $500, 000 to spend on expanding capacity. If this investment will buy 500 units of truck capacity, 1000 units of machine capacity, or 300 units of steel capacity, what would be the best investment?

 g) If the world market price of the imported materials needed to produce one unit of trucks were to increase by $400, what would be the optimal export mix for New France, and what would be the dollar value of their net exports?

Variables:

  X1 = Steel production for export (EXSTEE),

  X2 = Machinery production for export (EXMACH),

  X3 = Truck production for export (EXTRUC),

  X4 = Total steel production (TOSTEE),

  X5 = Total machinery production (TOMACH),

  X6 = Total truck production (TOTRUC)

Constraints:

 Steel output (STEEL)

Machinery output (MACHIN)

Truck output (TRUCK)

 Steel capacity (CAPSTE)

 Machinery capacity (CAPMAC)

Truck capacity (CAPTRU)

 Manpower available (AVAMAN)

Jean-Pierre Leveque has recently been named the Minister of International Trade for the new nation...-2

h) The Minister of Defense has recently come to Jean-Pierre and said that he would like to stockpile (inventory) an additional 10,000 units of steel during the coming year. How will this change the constraint equation STEEL, and what impact will it have on net dollar exports?

 i) A government R&D group has recently come to Jean-Pierre with a new product, Product X, that can be produced for export with 1.5 man-years of labor and 0.3 units of machinery for each unit produced. What must Product X sell for on the world market to make it attractive for production?

 j) How does this particular formulation deal with existing inventories at the start of the year and any desired inventories at the end of the year?

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