Another member of Jean-Pierre’s staff has presented an alternative formulation of New France’s…
Another member of Jean-Pierre’s staff has presented an alternative formulation of New France’s planning problem
as described in Exercise 3, which involves only three variables. This formulation is as follows:
Y1 = Total steel production,
Y2 = Total machinery production,
Y3 = Total truck production
Maximize z = 900(Y1 − 0.75Y2 − Y3) − 300Y1 + 2500(Y2 − 0.05Y1 − 0.10Y3) −150Y2 + 3000(Y3 − 0.80Y1 − 0.12Y2) − 500Y
Y1 ≤ 300,000,
Y2 ≤ 50,000,
Y3 ≤ 550,000,
0.5Y1 + 5Y2 + 3Y3 ≤ 1,200,000, Y1, Y2, Y3 ≥ 0.
a) Is this formulation equivalent to the one presented in Fig. of Exercise 3? How would the optimal solution here compare with that found in Fig.?
b) If we had the optimal solution to this formulation in terms of total production, how would we find the optimal exports of each product?
c) What assumption does this formulation make about the quantities and prices of products that can be exported and imported?
d) New France is considering the production of automobiles. It will take 0.5 units of steel, 0.05 units of machinery, and 2.0 man-years to produce one unit of automobiles. Imported materials for this unit will cost $250 and the finished product will sell on world markets at a price of $2000. Each automobile produced will use up .75 units of the country’s limited truck capacity. How would you alter this formulation to take the production of automobiles into account?