Question

1. A supervisor needs to produce widgets. Two machines are able to make the widgets. Machine A takes 2 hours to set up and can then make widgets at a rate of 80 per hour. The machine does not have to be stopped once it is running. Machine B takes 30 minutes to set up and can then widgets at the rate of 60 per hour, but every 2 hours the machine has to be stopped and lubricated. Lubrication takes 30 minutes. All costs are calculated at a rate of $40 per hour. Draw a chart to compare costs. Read from the chart:
   1. The least cost method to produce 150 widgets.
   2. The least cost method to produce 400 widgets.
   3. The earliest point at which the costs will be the same (in units)

Answer 1

For x number of widgets to be produced,

Total time of machine A = Setup time + Run time = 2 + x/80 hours

Total cost using machine A = 40*total time = 40*(2+x/80) = 80+x/2

Total time of machine B = Setup time + Lubrication time + Run time = 30/60 + x/60 + (30/60)*x/(60*2)

= 0.5+x/48

Total cost using machine B = 40*total time = 40*(0.5+x/48) = 20+5x/6

Data for graph

EXCEL FORMULA:

Chart is drawn using the above data as follows:

In the above graph, we see that for number of widgets less than 170, Machine B gives the lowest total cost.

a)

150 is less than the range (1.e. 0 to 170)

Therefore, Machine B gives the least total cost

Answer: machine B

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b)

400 is greater than than the range (1.e. 0 to 170)

Therefore, Machine A gives the least total cost

Answer: machine A

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c)

The earliest point at which the costs will be same is computed by equating the total cost equations of both machines

80+x/2 = 20+5x/6

Solving for x, we get,

5x/6-x/2 = 80-20

x/3 = 60

x = 180

Answer: 180