Question

Bus Econ 1.4.49 A company finds it can produce 5 heaters for $1550, while producing 10 heaters costs $2900. Express the cost, y, as a linear function of the number of heaters, X.

a) y = 290x + 1550
b) y = 290x - 1550
c) y = 290x
d) y = 1550x + 290

Answer 1

The cost, y, can be expressed as a linear function of the number of heaters, x, using the given information. The linear function is y = 70x + $1200.

Step-by-step explanation:

The cost, y, can be expressed as a linear function of the number of heaters, x, using the information provided. We can use the formula of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.

Based on the given information, when x = 5, y = $1550 and when x = 10, y = $2900. We can now calculate the slope using the formula m = (y2 - y1) / (x2 - x1).

Plugging in the values, we get m = ($2900 - $1550) / (10 - 5) = $350 / 5 = 70.

Therefore, the linear function that represents the cost is y = 70x + b. To find the y-intercept, we can substitute the values of x and y into the equation and solve for b. Using the first set of values, we get $1550 = 70(5) + b. Solving for b, we find b = $1550 - $350 = $1200.

Therefore, the linear function that represents the cost is y = 70x + $1200.