South African wildlife management officials13 must decide annual quotas (in thousands of tons)

for harvesting of pilchards, anchovies, and other fish of the pelagic family in the rich waters to the west of the Cape of Good Hope. One consideration is the maximization of fishing industry income, which is estimated at 110 rand/ton for pilchards, 30 rand/ton for anchovies, and 100 rand/

ton for other pelagic. Still, the harvest should leave the year-end populations of the 3 types of fish as large as possible. Scientists estimate that initial biomasses of the 3 types are 140,000 tons, 1,750,000 tons, and 500,000 tons, respectively. Due to differences in breeding characteristics, each thousand tons of pilchards harvested will deplete the population by 0.75 thousand tons, each of anchovies by 1.2 thousand tons, and each of other pilchards by 1.5 thousand tons. A final consideration is maintaining the ocean ecosystem. Important measures are the number of breeding characteristics, each thousand tons of pilchards harvested will deplete the population by 0.75 thousand tons, each of anchovies by 1.2 thousand tons, and each of other pilchards by 1.5 thousand tons. A final consideration is maintaining the ocean ecosystem. Important measures are the number of breeding pairs of penguins

(thousands), which is estimated as 70 + 0.60

(ending biomass of pilchards), and the number of such pairs of gannets (thousands), which is estimated at 5 + 0.20 (ending biomass of pilchards)

+ 0.20 (ending biomass of anchovies).

(a) Formulate a multiobjective LP to maximize all measures of success using the decision variables (i = 1, pilchards; i = 2, anchovies; i = 3, other pelagic)
xi !quota for fish type i 1thousand tons2 yi !ending biomass of fish type i 1thousand tons2

(b) Revise your formulation as a goal program with minimum targets for the 6 objectives being 38 million rands income, ending biomasses of 100, 1,150,000 and 250,000 tons, and ending breeding populations of 130,000 and 25,000 pairs. Give preemptive priority to maintaining the populations of the 3 types of fish.

(c) Enter and solve your goal program version using class optimization software.