Answer:
a. C(x) = 0.097x + 1.32
b. Fixed cost = $1.32
c. the total cost of producing 1000 cups is $98.32.
d. The total cost of producing 1001 cups is $98.417.
e. The marginal cost of any cup is $0.097. It means to produce one additional cup of coffee, the manager has to spend $0.097.
Explanation:
a. Find a formula for C(x)
Slope = (High cost - Low cost) / (High units - Low units) = (40.12 - 11.02) / (400 - 100) = 29.10/300 = 0.097
Using the equation form:
y = bx + a .......................... (1)
Where, using the high cost and high units:
y = cost = C(x) = $40.12
b = Slope = 0.097
x = units = 400
a = Fixed cost = ?
Substituting the values into equation (1) and solve for a, we have:
40.12 = (0.097 * 400) + a
40.12 = 38.80 + a
a = 40.12 - 38.80
a = 1.32
Therefore, we have:
C(x) = 0.097x + 1.32
b. What is the fixed cost?
From part a above, we have:
a = Fixed cost = $1.32
c. Find the total cost of producing 1000 cups
This implies that x = 1000
Substituting x = 1000 into the cost function C(x) = 0.097x + 1.32, we have:
C(1000) = (0.097 * 1000) + 1.32 = $98.32
Therefore, the total cost of producing 1000 cups is $98.32
d. Find the total cost of producing 1001
This implies that x = 1001
Substituting x = 1001 into the cost function C(x) = 0.097x + 1.32, we have:
C(1001) = (0.097 * 1001) + 1.32 = $98.417
Therefore, the total cost of producing 1001 cups is $98.417
e. What is the marginal cost of any cup and what does this mean to the manager.
The marginal cost of any cup is $0.097.
The meaning of the marginal cost to the manager is that to produce one additional cup of coffee, he has to spend $0.097.
