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Question & Answer: An expensive food-additive known to offset ultraviolet skin damage is manufactured…..

1. An expensive food-additive known to offset ultraviolet skin damage is manufactured at the Bayer pharmaceutical plant in Frankfurt Germany, where the acceleration of gravity is 9.814 m/s2. The additive is sold directly from the factory at a price of $1000 per ounce. The point-of-sale weight is determined by weighing the additive on a precise German-made spring-scale. An aging baby-boomer from Pueblo CO has decided to set up a small retail shop so that he can sell the food-additive to the captive audience of wealthy hikers passing through the Lhotse Base Camp at Mt. Everest, elevation 23,700. However, at this geographic location, the acceleration of gravity is only 9.764 m/s2. (a) Ignoring overhead costs (transportation, packing, personnel, etc.), what price per ounce (as measured by weighing the additive on a spring-scale at the base camp) must he charge in order to break even? Please report your answer nearest dollar. (Note: The value of g that was used to calibrate the precise the scales described in this problem is 9.80665 m/s2. I am not sure if this matters.) (b) What will be his break-even price if a beam-balance is used to weigh the additive sold (at both locations), instead of a spring-scale?
An expensive food-additive known to offset ultraviolet skin damage is manufactured at the Bayer pharmaceutical plant in Frankfurt Germany, where the acceleration of gravity is 9.814 m/s^2. The additive is sold directly from the factory at a price of $1000 per ounce. The point-of-sale weight is determined by weighing the additive on a precise German-made spring-scale. An aging baby-boomer from Pueblo CO has decided to set up a small retail shop so that he can sell the food-additive to the captive audience of wealthy hikers passing through the Lhotse Base Camp at Mt. Everest, elevation 23, 700′. However, at this geographic location, the acceleration of gravity is only 9.764 m/s^2. (a) Ignoring overhead costs (transportation, packing, personnel, etc.), what price per ounce (as measured by weighing the additive on a spring-scale at the base camp) must he charge in order to break even? Please report your answer nearest dollar. (b) What will be his break-even price if a beam-balance is used to weigh the additive sold (at both locations), instead of a spring-scale?

Expert Answer

Answer
Mass is a fundamental quality of an object that does not change, and is measured in ounces. Weight is mass times gravitational acceleration.
at the plant, gravity 9.814
cost of additive $        1,000 per ounce
gravity at the base camp 9.764 mt sq sec
a) the ration of the weight at the camp and factory is
1.005
Hence, at the base camp, the additive should be sold at 1.005 times the cost, to breakeven.
Cost at factory $        1,000 per ounce
Breakeven price at bas camp(=1000*1.005) $ 1,005.12 per ounce
(Please note, at breakeven there is no profit or loss, hence, only the cost should be recovered to breakeven.)
b)
Spring scales measure weight (force) by balancing the force due to gravity against the force on a spring, whereas a beam-balance compares masses by balancing the weight due to the mass of an object against the weight of a known mass
Thus, if a beam-balance is used then, the gravity will not affect the measured weight of the additive, provided the weights used to measure at both locations have same calibration.
hence, to breakeven,
price at base camp= $        1,000 per ounce

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