Question

EXCEL SOLVER: A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? NEED TO ANSWER IN EXCEL SOLVER NEED HELP PLEASE

Answer 1

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Assume that we get x tons of source A and y tons of source B (perday)
obviously: x0 and y0
the cost : C=20x+10y 80
given condition : y2x
we need to maximize the amount of gold extracted : S=2x+3y
we graph:


y2x A 20x+10 CO


the region of (x,y) is the region in triangle ABC where A,B,C arethe critical points
A(0,0) ,B(2,4) ,C(4,0)
the maximize occur at certain critical point so we can substitute:
S(A)= 0    ;S(B)=16 ;S(C)=8 (B is theintersection of y=2x and 20x+10y=80)
=> S maximize at B,when x=2 and y=4
so one day,he should process 2 tons of source A and 4 tons ofsource B to get maximum is 16 oz. of goal .

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