Question

A manufacturer keeps track of her monthly costs by using a cost function this assigns a total cost for a given number of manufactured items X the function is C(x)=5,000 + 1.3x

what is the reasonable domain of this function what is the cost of 2,000 items that the cost must be kept below 10,000 this month what is the greatest number of items she can manufacturer need these answers ASAP please help

Answer 1

a)Domain is all positive integers.

b)C(2000)=$7600

c) For C(x)<10000, less than 3846 items should be manufactured.

Explanation:

Given that cost function is C(x)=5000+1.3x, where x is the number of manufactured items.

a) The domain of C(x) means the range of values x can take. Since x is the number of manufactured items, it cannot be negative and fraction.

Hence domain is all positive integers.

b)To find the cost of 2000 items, we should plugin x=2000 in C(x).

That is cost of 2000 items, C(2000)=5000+1.3(2000)=5000+2600=$7600

c) We are asked to find the number of items such that cost is kept below 10,000 that is C(x)<10000

5000+1.3x<10000

Subtract 5000 from both sides

1.3x<5000

Divide with 1.3 on both sides

`x<(5000)/(1.3)`

x<3846.2

Hence number of items must be less than 3846 for C(x)<10000