An aerospace machining shop has exactly 500 sq. ft. of space to store two kinds

Question

An aerospace machining shop has exactly 500 sq. ft. of space to store two kinds of machined parts: gears and pistons. The appropriate data for these parts is given below. The annual interest rate used for computing holding costs for both the parts is 25% Piston (2) Gear () Annual demand (in units) Setup cost for production Cost per part Space required per part 100 $1,000 $20 1 sq. ft. 400 $1,000 $40 2 sq. ft. ? K (a) (10 points) What are the optimal quantities that should be manufactured for both parts? (b) (5 points) Is the solution for part (a) unique? (c) (5 points) Compute average annual cost at optimal solution.

Explanation / Answer

This question can be resolved through solver and the following equations have to be used

Let the number of gera to be produced is x and the no of piston be y

x<= 100

y<= 400

x+ 2y =500

20x + 40y + 1000( if x>0) + 1000( if y>=0)= Total cost

Interest rate = 0.25*(20x + 40y)

We get multiple solution for these equations

few solutions are x = 100, y =200

x =0 and y =250 and all values of y will range [200,250] and x will range from all even numbers between [0,100].

Hence the solution is not unique

Average annual cost for the same is 14500 ( putting x = 100 and y =200) in both equation of total cost and interest rate. The cost will remain same for all the values except for x =0 and y =250 in that case it is 13500.

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