Question

Cost equationcost of producing 7 unitswhat is the break point

Answer 1

Part A: C(x) = 0.068x+0.8

Part B: 1.28

Part C: 9.76

Explanation:

Part A:

The cost C equals

cost = revenue - profit

`C(x)=R(x)-P(x)`

which is

`C(x)=0.15x-(0.082x-0.8)`
`C(x)=0.15x-0.082x+0.8`
`\boxed{C\mleft(x\mright)=0.068x+0.8}`

Part B:

The cost of producing 7 units is found by putting in x = 7 into the above equation. This gives

`C(7)=0.068(7)+0.8`
`C(7)=1.28`

Hence, the cost of producing 7 items is 1,28 million dollars.

Part C:

To break even, the cost must equal the revenue

`R(x)=C(x)`

or

`0.15x=0.068x+0.8`

subtracting 0.068 from both sides gives

`0.082x=0.8`

dividing both sides by 0.082 gives

`\boxed{x=9.76}`

which is the break-even point