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math problems

 
 
Reply Wed 9 Apr, 2008 01:33 pm
I have two math problems that need your help,
1. A machine part is manufactured at a unit cost of $0.40 for materials and $0.15 for direct labor. An investment of $500,000 in tooling is required. The order calls for 3 million pieces.
Halfway through the order, a new method of manufacture can be put into effect that will reduce the unit costs to $0.35 for material and $0.14 for direct labor?-but will require $100,000 for additional tooling. This tooling will not be useful for future orders.
Other costs are allocated at 2.5 times the direct labor costs.
Complete an analysis.


2. In the design of a cold-storage warehouse, the specifications call for a maximum heat transfer through the warehouse walls of 30,000 joules per hour per square meter (30,000 joules/hr/m2) when there is a 30oC temperature difference between the inside surface and the outside surface of the insulation.
The two insulation materials being considered are as follows:

Insulation Material Cost per Cubic Meter Conductivity
(J-m/m2-oC-hour)
Rock wool $12.00 125
Foamed insulation $15.00 100

The basic equation for heat conduction through a wall is:
Q = (K(ΔT))/L
Where:
Q = heat transfer, in J/hr/m2 of wall.
K = conductivity in J-m/m2-oC-hour.
ΔT = temperature difference between the two surfaces in oC.
L = thickness of insulating material, in meters.

What are the total costs of each insulation material?

Thanks in advance
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Kayyam
 
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Reply Thu 10 Apr, 2008 11:37 pm
Re: math problems
rockerpham wrote:
I have two math problems that need your help,
1. A machine part is manufactured at a unit cost of $0.40 for materials and $0.15 for direct labor. An investment of $500,000 in tooling is required. The order calls for 3 million pieces.
Halfway through the order, a new method of manufacture can be put into effect that will reduce the unit costs to $0.35 for material and $0.14 for direct labor?-but will require $100,000 for additional tooling. This tooling will not be useful for future orders.
Other costs are allocated at 2.5 times the direct labor costs.
Complete an analysis.


cost1 = 0.55*3e6 + 5e5 = 2.15e6
cost2 = 0.55*1.5e6 + 5e5 + 0.49*1.5e6 + 1e5 = 2.16e6

Sounds like option 2, ignoring "other costs", will save $10,000. Future orders are irrelevant.

Quote:
2. In the design of a cold-storage warehouse, the specifications call for a maximum heat transfer through the warehouse walls of 30,000 joules per hour per square meter (30,000 joules/hr/m2) when there is a 30oC temperature difference between the inside surface and the outside surface of the insulation.
The two insulation materials being considered are as follows:

Insulation Material Cost per Cubic Meter Conductivity
(J-m/m2-oC-hour)
Rock wool $12.00 125
Foamed insulation $15.00 100

The basic equation for heat conduction through a wall is:
Q = (K(ΔT))/L
Where:
Q = heat transfer, in J/hr/m2 of wall.
K = conductivity in J-m/m2-oC-hour.
ΔT = temperature difference between the two surfaces in oC.
L = thickness of insulating material, in meters.

What are the total costs of each insulation material?

Heat transfer:
3e5 = K*30/L
Costs per square meter:
cost1 = 12*L1 = 12*125*30/3e5 = 0.15
cost2 = 15*L2 = 15*100*30/3e5 = 0.15

Same cost dude. Might as well go with the foamed insulation since it takes up less space and is easy to install.

/Kayyam
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