Problem 2 [250] imum has recently been named the Minister of International Trade
ID: 356090 • Letter: P
Question
Problem 2 [250] imum has recently been named the Minister of International Trade (MIT) for a new nation c BlakPanther. In connection with this posit by maximizing the net dollarv defined as exports less the cost of all materials imported by the country.) ion, she has decided that the welfare of the country could best be served BlakPanther has traditionally made three products for export: steel, heavy machinery, and trueks. For the coming year, Dr. Optimum 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 0.05 units of machinery 0.08 units of trucks .2.0 units of ore purchased on the world market for $100/unit Other imported materials costing $100
Explanation / Answer
(a)
The optimal production and export mix is as follows -
The total net dollar value of this plan = $176,750,000
(b)
The investment is $650,000. Only machinery capacity increase surpasses this cost. So, upgrading machinery is the only suitable choice.
(c)
The present coefficient is -500. The allowable decrease is $4,287. Here, the proposed decrease is only $350.
So, the optimal solution will not change. However, the objective value will reduce to:
$176,750,000 - $350*30,000 = $166,250,000
(d)
The RHS of the Steel ) constraint will change from 0 to 7,000.
7,000 is less than the allowable increase which is 231500. So, the shadow price of -900 will remain unchanged. The profit or net export will reduce to:
$176,750,000 - $500*7,000 = $173,250,000
(e)
The allowable decrease for RHS of this constraint is 71,0000 i.e. up-to 1,200,000 - 71,0000 = 490,000 labor hours, the shadow price of 0 will be intact.
Here the reduced value of RHS is only 750,000. So, no change will be there in the net export $.
Total Produced Exported Steel 300000 232500 Machinery 50000 32000 Truck 30000 0Related Questions
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