A college wants to produce an effigy for the student carnival. Preliminary studies made it possible to establish that the production of these effigies requires fixed costs of $2,008 and variable costs (materials, labor, energy) of $0.90 per effigy. One of the requirements of the college being not to make a deficit, he had a market study carried out. It appears from this study that by selling these effigies for $3.75 we can hope to sell them 1,000, whereas by setting the price at $2.50, the potential sales are 3,000. a) Express the demand in terms of the selling price and represent graphically this function. b) Express the cost of production as a function of the selling price. c) Express the income in terms of the selling price and determine the price that the college should fix to maximize the income from this sale of effigies.
1. A college wants to produce an effigy for the student carnival. Preliminary studies
made it possible to establish that the production of these effigies requires fixed costs of $2,008
and variable costs (materials, labor, energy) of $0.90 per effigy. One of the
requirements of the college being not to make a deficit, he had a market study carried out.
It appears from this study that by selling these effigies for $3.75 we can hope to sell them
1,000, whereas by setting the
a) Express the
graphically this function.
b) Express the cost of production as a function of the selling price.
c) Express the income in terms of the selling price and determine the price that the
college should fix to maximize the income from this sale of effigies.
d) Represent the income function and the cost function on the same system of axes
and determine the prices corresponding to the break-even thresholds and number
effigies which will then be sold.
e) Express the profit as a function of the selling price.
f) Determine the price that the college should set to maximize the profit of this
sale.
Given information
Fixed cost of producing effigy = $2008
Variable cost = $0.90 per effigy
When
Selling price = $3.75, Q = 1000
Selling price = $2.50, Q = 3000
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