Question

5. We are asked to choose among various carbon reduction strategies to maximize the tons of atmospheric carbon removed subject to various constraints strategy 1 strategy 2 strategy 3 maximum 1000 600 23 125 100 150 110 capital 100 50 labour space habitat damage tons carbon removed 15 21 26 There is an additiona political decision that we must choose at least 1.5 units of Strategy 1 Here is the problem formulation for LINDO MAX 15 STRAT1+ 21 STRAT2+ 26 STRAT3 SUBJECT TO CAPITAL) LABOUR) 100 STRAT! + 125 STRAT2 + 150 STRAT3 <= 50 STRATI + 100 STRAT2 + 110 STRAT3 <= 600 2 STRATI + 3 STRAT2 + 4 STRAT3 23 3 STRATI + STRAT2 + STRAT3 <= 8 1000 SPACE) HABITAT) POLITICS) STRAT!〉= 1.5 END

Answer 1

Solution)

	St1	st2	st3	max	1.5 st1
capital	100	125	150	1000	150
labour	50	100	110	600	75
space	2	3	4	23	3
habitat damage	3	1	1	8	4.5
tons carbon removed	15	21	26		22.5

optimal solution is as below without the constraint of 1.5 st1

capital	130.4348	228.2609	339.1304	697.8261
labour	65.21739	182.6087	248.6957	496.5217
space	2.608696	5.478261	9.043478	17.13043
habitat damage	3.913043	1.826087	2.26087	8
tons carbon removed	19.56522	38.34783	58.78261	116.6957

if 1.5 ST1 is required oprimal solution is as below

150	200.2877	297.5703	647.8581
75	160.2302	218.2182	453.4484
3	4.806905	7.935209	15.74211
4.5	1.602302	1.983802	8
22.5	33.64834	51.57886	107.7272

max=15s1+21st2+26st3

A) now the carbon removed by st1 is reduced from 15 to 14

in the optimal solution st1 is used 1.5 times as its corbon reduction is reduced by 1 therefore thje total carbon reduction will be reduced by 1.5 in the optimal solution.

B)If habitat damage is allowed to go from 8.5 to 8 then coefficient of strategy 1 can be increased leading to increase in reduction of carbon footprint in optimal solution as below

150	228.2609	339.1304	717.3913
75	182.6087	248.6957	506.3043
3	5.478261	9.043478	17.52174
4.5	1.826087	2.26087	8.5
22.5	38.34783	58.78261	119.6304

Resulting an increase of 11.9 in the reduction ofcarbon foot print/

C) Total cost is $ 36951.83 and total carbon foot print reduced =107.72 leading to cost per unit of carbon redution = $343 which is less than $400

D) With the new strategy habitat damage is 1unit which is less than stragey-1 of 3 units. As space id the deadlock in the optimal solution , we will include the new strategy in the optimal solution and yes we will investigate further to include tihis in our optimal solution.