.
(1) The optimal production quantities are 400, 200, 400 and 0 at plants 1, 2, 3 and 4 respectively and the cost of production is 11600.
(2) The cost of producing one more vehicle or the savings resulting from reducing production by one unit is 30 (shadow price for the ``Total'' constraint.
(3) The change in cost is 2 (thousands of dollars) which is less than the allowable decrease of 1E+30; hence the solution remains the same. The solution is valid in the range (10 - 1E+30, 10 + 2) i.e., .
(4) The shadow price is zero; hence we will not be willing to pay anything for a labor hour.
(5) The relevant shadow price is 4; the value of reducing the limit to 200 from 400 is 200*4 i.e., 800 and the value of reducing the limit to 0 is 400*4 i.e., 1600 (since these decreases are within the allowable decrease of 400). Similarly, the cost of increasing the limit by 100 would cost 100*4 i.e., 400 (the allowable increase is 100). An increase of 200 is greater than the allowable increase (100) and further analysis is required to see the effect of such an increase.
(6) One more unit of raw material is worth 5 (shadow price) and we would be willing to buy 300 more units (the allowable increase is 300) at this price. Further analysis is required to arrive at the costfor increases beyond 300 units.
(7) Using the shadow prices of the constraints, the maximum cost the new plant can have in order to be considered for usage is 0 + 4(-5) + 0 + 1(30) = 10.
(8) Plant 4's cost has to reduce by more than 7 (allowable decrease) to be considered for usage (for the solution to change).
(9) The allowable increase is 1E+30; hence the costs can increase to 
and the solution would not change.