College

Find a linear function that models the cost, \( C(x) \), to produce \( x \) toys given the rate of change and initial output value.

- The cost to produce plastic toys increases by 90 cents per toy produced.
- The fixed cost is 40 dollars.

\[ C(x) = 0.90x + 40 \]

Write a linear model for the amount of usable fabric sheeting, \( F(t) \), manufactured in \( t \) minutes given the rate of change and initial output value.

- Fabric sheeting is manufactured on a loom at 7.25 square feet per minute.
- The first five square feet of the fabric is unusable.

\[ F(t) = 7.25t - 5 \]

Where \( F(t) \) is the amount of usable fabric sheeting manufactured in \( t \) minutes.

Answer :

Answer:

C(x) = $40 + 0.9x

F(t) = 7.25t - 5

Step-by-step explanation:

Given that :

C(x) = Cost model to produce x toys

Fixed cost of production = $40

Rate of change = 90 cent per toy produced.

A linear model will take the form :

F(x) = bx + c ;

Where ; b = rate of change or slope ; c = intercept or initial value

Therefore, a linear cost model will be :

Cost model to produce x toys = fixed cost + (rate of change * number of toys)

C(x) = $40 + 0.9x

2.)

F(t) = amount of usable factory sheets manufactured in t minutes :

Rate of production = 7.25 ft² / minute

Number of unusable fabric sheeting = 5 ft²

The function, F(t) :

F(t) = 7.25t - 5

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