Concept explainers
(a)
The equation models the costs of producing x pair of item-S.
The cost function model is
Given:
The annual cost C of making x pairs of items is
Concept Used:
The cost function is made up of two quantity, one a variable quantity that depends on numbers of productions and other is constant, that is fixed.
Calculation:
If
Thus, the equation models of the costs of producing x pair of item is:
Conclusion:
The cost function model is
(b)
The equation models the revenue of selling x pair of item-S.
The equation models the revenue of selling x pair of item-S is
Given:
The annual cost C of making x pairs of items is
Concept Used:
The revenue is the amount generated by selling the item.
Calculation:
The item-C is sold at
Hence, the equation models the revenue of selling x pair of item-S is:
Conclusion:
The equation models the revenue of selling x pair of item-S is
(c)
The numbers of pairs to be produce and sold in order to break even.
The graph of equation model cost and revenue intersecting at break-even.
Given:
The annual cost C of making x pairs of items is
Concept Used:
The break-even point arrives when cost and revenue are equal.
Calculation:
The cost and revenue function for x pairs of items is
If x is the numbers of pairs in order to break even, then
Solve
Hence, the numbers of pairs to be produce and sold in order to break even is
Conclusion:
The numbers of pairs to be produce and sold in order to break even is
(d)
The graph of equation that models the cost and revenue and interprets the break-even point.
The numbers of pairs to be produce and sold in order to break even is
Given:
The annual cost C of making x pairs of items is
Concept Used:
Plot the points on graph obtained by choosing different values of x and join the points.
Calculation:
The cost function is
To graph the functions, compute the values for different values of x :
The points are plotted as follows:
Interpretation:
The graph of two equation of cost and revenue model intersect at
Conclusion:
The graph of equation model cost and revenue intersecting at break-even.
Chapter 1 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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