Question 1

An Indian manufacturer establishes that its total cost per item function (in Indian Rupees, INR) is given by C = 6000x^-1 + 2.5+ 0.03x. Work out the volume that minimises average cost (cost per item). A) 2,000 B) 20,000 C) 200,000 D) 2,000,000

Accepted Answer

200,000

Question 2

A Ghanaian company establishes that for one of its products = 350 and that = 600 - 2.5x. Which of the following options represents the correct function?&#10;A) = 250 + 2.5x&#10;B) = 950 - 2.5x&#10;C) = 250 - 2.5x&#10;D) You cannot work this out from the data given

Accepted Answer

The correct function is = 250 - 2.5x because it satisfies the given conditions: = 350 when x = 0, and = 600 - 2.5x when x = 100.

Question 3

Which of the following statements regarding maximum profit is TRUE?&#10;A) The maximum profit level is  &#10;B) The maximum profit level is when  &#10;C) The maximum profit level is when   &#10;D) None of these are correct

Accepted Answer

The maximum profit level is when

Question 4

Establish the profit if a retailer can purchase 150 jackets at 270 Emirati Dirham (AED) and sell them for AED 360.&#10;A) AED 10,500&#10;B) AED 11,500&#10;C) AED 12,500&#10;D) AED 13,500

Accepted Answer

The profit for each jacket is AED 360 - AED 270 = AED 90. For 150 jackets, the total profit is 150 * AED 90 = AED 13,500.

Question 5

An Egyptian manufacturer has calculated a total cost function of C = 15 + 6x and a total revenue function of R = 3x + 2x². Calculate the level of sales that maximises profit (x represents volume in '000s of units).

A) 750
B) 800
C) 850
D) 900

Accepted Answer

To maximize profit, set marginal cost equal to marginal revenue. The derivative of the cost function C = 15 + 6x is 6. The derivative of the revenue function R = 3x + 2x^2 is 3 + 4x. Setting 6 = 3 + 4x gives x = 750.

Question 6

A company establishes that for one of its products = 400 and that = 850 - 3x. Calculate the volume (x) at which profit is maximised.&#10;A) 150&#10;B) 160&#10;C) 170&#10;D) 180

Accepted Answer

To maximize profit, set marginal cost equal to marginal revenue. Given cost = 400 and revenue = 850 - 3x, solve 850 - 3x = 400 to find x = 150.

Question 7

If the price function for a given product is p_r(x) = 10 - 3x which of the following options represents the correct total revenue function? A) R = 10x + 3x² B) R = 10x - 3x² C) R = 10x - 3x D) R = 10x + 3x

Accepted Answer

The total revenue function, R, is found by multiplying the price function, p(x), by the quantity sold, x. Given p(x) = 10 - 3x, the total revenue function is R = x(10 - 3x) = 10x - 3x^2.

Question 8

Which of the following options is NOT a component of the total cost function?&#10;A) Special costs&#10;B) Fixed costs&#10;C) Travel costs&#10;D) Variable costs

Accepted Answer

Travel costs are not a component of the total cost function.

Question 9

What is the breakeven point if P = 48x - 3x² (x is hundreds of products) A) 200 B) 300 C) 400 D) 500

Accepted Answer

The breakeven point occurs when total revenue equals total costs, which is represented by the equation P = 0. Substituting P = 0 into the given equation, 0 = 48x - 3x^2, simplifying gives 3x^2 = 48x, which further simplifies to x^2 = 16x. Dividing both sides by x (assuming x ≠ 0) gives x = 16. Since x represents hundreds of products, the breakeven point is 16 * 100 = 1600 products. However, none of the options match this result, suggesting a possible misunderstanding or typo in the question or options. Based on the closest available option, 400 (C) would be chosen, but it's important to note the discrepancy.

Question 10

If demand for a product is 3,500 when the price is 7 Turkish Lira (TRY) and falls to 1,000 when the price is TRY 18 which of the following options is the correct linear demand function? A) p_r(x) = 22.4 - 0.0044x B) p_r(x) = 22.4 + 0.0044x C) p_r(x) = -22.4 - 0.0044x D) p_r(x) = -22.4 + 0.0044x

Accepted Answer

The correct linear demand function can be found by using the two given points (3500, 7) and (1000, 18) to calculate the slope (m) and then using one of the points to solve for the y-intercept (b) in the equation p = mx + b. The slope m = (18 - 7) / (1000 - 3500) = 11 / (-2500) = -0.0044. Using the point (3500, 7), we can solve for b: 7 = -0.0044(3500) + b, which gives b = 22.4. Thus, the correct equation is p = 22.4 - 0.0044x.

Deck 28: Cost, Revenue and Profit Functions