Answer:
1)A) Minimize C = 40x + 100y.
2) d) 7x + 8y ≤ 190, 5x + 4y ≤ 22, x ≥ 0, y ≥ 0.
3) B) Min C = 295x + 416y; s.t 23x + 15y ≥ 154, 17x + 25y ≥ 140, x ≥ 0, y ≥ 0.
Step-by-step explanation:
1) Energize pills cost 40 cents each, while Excel pills cost 100 cents each. If x represent the energize pills and y represent the excel pills, the objective function would be:
minimize cost = cost of energize pill + cost of excel pill
Minimize cost = 40x + 100y
2) Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce.
7 hours of assemble time to produce a mountain bike and 8 hours of assemble time to produce a racing bike. Since the company has at most 190 hours for assemble time, it can be represented as:
7x + 8y≤ 190
5 hours of mechanical tuning to produce a mountain bike and 4 hours of mechanical tuning to produce a racing bike. Since the company has at most 22 hours for mechanical tuning, it can be represented as:
5x + 4y ≤ 22
Also assemble time and mechanical time must be greater than 0, hence:
x ≥ 0, y ≥ 0
3) The fieldwork constraint can be represented as:
23x + 15y ≥ 154
The time to be spent at university research center can be represented as:
17x + 25y ≥ 140
Both fieldwork time and time spent at university research center mut be greater than 0, hence:
x ≥ 0, y≥ 0
The cost equation is:
Minimize cost = 295x + 416y
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