Final answer:
The cost equation is y = 70x + 6000. The fixed cost is $6000. The marginal cost of production is $70. Sketch the graph of the equation to visualize the relationship between cost and the number of radios produced.
Step-by-step explanation:
a. To find the cost equation, we can use the formula: y = mx + b, where y represents the cost, x represents the number of radios, m represents the slope, and b represents the y-intercept (fixed cost).
We are given two points on the cost equation: (20, 7400) and (50, 9500). Using these points, we can calculate the slope (m) as follows: m = (y2 - y1) / (x2 - x1) = (9500 - 7400) / (50 - 20) = 2100 / 30 = 70.
Now, we can substitute the slope and one of the points into the cost equation formula to find the y-intercept (b): 7400 = 70 * 20 + b. Solving for b gives us b = 7400 - 70 * 20 = 7400 - 1400 = 6000.
Therefore, the cost equation is y = 70x + 6000.
b. The fixed cost is represented by the y-intercept of the cost equation, which is $6000.
c. The marginal cost of production is the change in cost for producing an additional unit. In this case, the marginal cost is equal to the slope of the cost equation, which is $70.
d. To sketch the graph of the cost equation, plot the points (20, 7400) and (50, 9500) on a graph and draw a straight line through these points. The y-axis represents the cost and the x-axis represents the number of radios.