A computer aided drafting (CAD) instructor at a community college wants to use his rapid prototype...

A computer aided drafting (CAD) instructor at a community college wants to use his rapid prototype machine to produce demo items for a seminar on engineering technology. He plans to bring two different types, a Golden Ruler and a Fibonacci Gauge. He will bring at least 20 of each. he has 45 cubic inches of filler and 95 cubic inches of material available to make the demos, but only has 86 hours of free time to run the machine. he is able to save time by running the demos in batches. Use the information in the table to determine how many of each demo item he needs to bring while minimizing the total cost. Set up but do not solve.

Demo Type	Material (in³/batch)	Filler (in³/batch)	Batch Time (hrs)	Batch size	Batch cost ($)
Golden Ruler	10	3	7	8	22
Fibonacci Gauge	7.5	5	8.5	10	20

Solutions

Expert Solution

Answer: det a number of Golden Ruler batches, Y = number of fibonacci hauges, our job is to minimize total cost, 2= 22x+2y Under the constraints 10x +7.54 <45 (Material) 3x + 5y {as (filler) 7x+8.54 286 hours) x>, and y=2 (He needs at least 3 batches to produce a mininum of 20 Golden Ruless, at least 2 batches of fibonacci Ganges, also to meet the minimum of 20). 402 + 754 $ 45 84 1120, 26,667) 3 x + 2 y = 95 hot + Body = 86 A 124,0) -30 -20 o 10 20 30 yo tot

of 20 22x, troy, 22(20) +20 (20) = 440+400=840 22(24) + 20 (20) - 528 +400-928 22(20) + 20 (26.667) = 440+533.34 a = 913.34 26.667 The set of feasible boints is bounded. Cost of minimal, $ 106 at (3,2), That is, 3 batches of Golden Rulers (24 GR's), and 2 batches of fibonacci Gange

milcah answered 1 year ago

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