Answer:
a) GH¢15x
b) GH¢15
Explanation:
a) To find the cost function, C(x), given that it is linear, we need to find the slope and y-intercept of the line that represents the cost to produce x units of the product. We can use the point-slope form of a line to find the cost function: C(x) = mx + b, where m is the slope and b is the y-intercept.
We have two points: (100, GH¢1,500) and (0, GH¢0), which represents the cost to produce 100 units and 0 units, respectively. The slope can be found by dividing the change in y by the change in x:
m = (GH¢1,500 - GH¢0) / (100 - 0) = GH¢15
The y-intercept can be found by plugging in one of the points and solving for b:
GH¢1,500 = (GH¢15)(100) + b
GH¢1,500 = GH¢1,500 + b
b = GH¢0
So the cost function is C(x) = GH¢15x + GH¢0.
b) To find the average cost per item to produce 50 units and 300 units, we need to divide the total cost by the number of units produced.
For 50 units:
C(50) = GH¢15 * 50 + GH¢0 = GH¢750
Average cost = C(50) / 50 = GH¢15
For 300 units:
C(300) = GH¢15 * 300 + GH¢0 = GH¢4,500
Average cost = C(300) / 300 = GH¢15