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5. Let f(I) = - 3000x + 60000 be a linear depreciation function of a machine to operate a factory where


a is the number of years, I = 0 means the present time (now), and f(z) in dollars.


a. Find the purchasing price of the machine i.e., the present value of the machine.


b. Find the book value of the machine after 2 years, i.e., I = 2.


c. If the machine will be used for 15 years only, then find the scrap value of the machine, i.e., x = 15


6. Let C(2) = 7 + 1000 be the cost function and R(a) = 120 be the revenue function depending on the quantity of a product


a. Find the unit cost of the product.


b. Find the fixed cost of the product.


c. Find the profit function of the product.


d. Find the break even point of the product.

Answer :

For the given linear depreciation function f(I) = -3000x + 60000, where I represents the number of years and f(I) represents the value of the machine in dollars at that time, we will determine various values and functions related to the machine's depreciation and the product's cost and revenue.

a. To find the purchasing price or present value of the machine, we evaluate the function at I = 0: f(0) = -3000(0) + 60000 = $60000.

b. To find the book value of the machine after 2 years (I = 2), we evaluate the function at I = 2: f(2) = -3000(2) + 60000 = $54000.

c. To find the scrap value of the machine after 15 years (I = 15), we evaluate the function at I = 15: f(15) = -3000(15) + 60000 = $15000.

For the cost function C(I) = 7 + 1000 and revenue function R(I) = 120, where I represents the quantity of the product:

a. The unit cost of the product is the cost per unit and is given as $1000.

b. The fixed cost of the product is the cost incurred regardless of the quantity produced and is given as $7.

c. The profit function P(I) is calculated by subtracting the cost function from the revenue function: P(I) = R(I) - C(I) = 120 - (7 + 1000).

d. The break-even point of the product is the quantity at which the revenue equals the cost, i.e., when P(I) = 0. To find the break-even point, we set the profit function equal to zero and solve for I.

Learn more about break-even analysis here: brainly.com/question/30837449

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