Question

You need a total of 60 pounds of two commodities costing $1.35 and $2.85 per pound.
A) Verify that the total cost is y = 1.35x + 2.85(60 - x), where x is the number of pounds of the less expensive commodity.
Let x be the number of pounds of the commodity costing $1.35 per pound. Because there are_____pounds total, the amount of the second commodity is______. The total cost, in dollars, is y = 1.35x + 2.85(60 - x).
B) Find the inverse function of the cost function.
What does each variable represent in the inverse function?
1) X represents the commodity costing $1.35 per pound and Y represents the commodity costing $2.85 per pound.
2) X represents pounds and Y represents cost.
3) X represents the commodity costing $2.85 per pound and Y represents the commodity costing $1.35 per pound.
4) X represents cost and Y represents pounds.
5) X represents the commodity costing $1.35 per pound and Y represents cost.
C) What is the domain of the inverse function?
Validate or explain your answer using the context of the problem.
1. The domain of the inverse function is equal to the range of the original function.
2. The domain of the inverse function is equal to the domain of the original function.
3. The domain of an inverse function is always R.
D) Determine the number of pounds of the less expensive commodity purchased when the total cost is $78.

Answer 1

Answer: provided in the explanation section

Step-by-step explanation:

We will take this problem step by step to ensure we have easy understanding of the problem at hand.

(a). taking x as the number of pounds of the commodity costing $1.35  per pound.

Also since we have 60 pounds as total

The amount of second commodity is 60 - x

then the total cost (in dollars) is

y = 1.35x + 2.85(60 - x)

(b). since we have that;

y = 1.35x + 2.85(60 - x)

solving for y gives

y = 1.35x + 171 - 2.85x

y = 171 - 1.5x

doing exchange of variables y and x we have;

x = 171 - 1.5y

where;

1.5y = 171 - x

y = 171 - x / 1.5

• f(x) = y
• and y = f⁻¹(x)

f⁻¹(x) = 2/3 [171 - x]    ------------- (1)

Here x represents the cost and y represents the pounds

(c). Given that less commodity is purchased, the Cost will be at  its lowest and will be 60 (1.35) = $81.

Also, if only the more expensive commodity is purchased, the Cost will be at its maximum and will be 60(2.85) = $171

• Therefore the domain of inverse becomes [81,171]

That is to say that the domain of inverse function is equal to the range of original  function.

(d). plug in x = $78 in the inverse function

where y = 2/3 [171-78]

y = 2/3[93] = 2[31]

y = 62

The number of pounds of the less expensive commodity purchased when the total cost is $78 is given as

y = 62

cheeers i hope this solution was helpful