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1. The manager of a restaurant found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12. Assume the cost is C(x)is a linear function of x, the number of cups produced a. Find the formula for C(x) b. What is the fixed cost c. Find the total cost of producing 1000 cups d. Find the total cost of producing 1001 cups e. What is the marginal cost of any cup and what does this mean to the manager

Sagot :

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.

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