Answer:
A. The point represents the turning point of the graph
B. The cost of making 4,000 bicycles is $265,000
The slope of the cost function, F(x) = 1.25 + 0.35·x, is less than the average slope of the graph of the total profit for sales
C. The company should plan on making fewer than 4,000 bicycles, to maximize profit
Explanation:
A. The point represents the turning point after which increase in the x-coordinate values leads to a decrease in the y-coordinate values
B. The cost function is presented as follows;
F(x) = 1.25 + 0.35·x
Where;
F(x) = The cost in hundreds of thousands of dollars of making 'x' (in thousands) bicycles
x = The number of bicycles made in thousands
The cost of making 4,000 bicycles is given by plugging in x = 4(thousand) in F(x) = 1.25 + 0.35·x, as follows;
F(x) = 1.25 + 0.35·x
∴ F(4) = 1.25 + 0.35 × 4 = 2.65
Therefore, the cost of making 4,000 bicycles = 2.65 × $100,000 = $265,000
The slope of the cost function, F(x) = 1.25 + 0.35·x, is given by the coefficient of 'x' which is 0.35
The average slope of the graph of the profit function is ((3.5 - 0)/(4 - 0)) = 0.875
The slope of the cost function is less than the average slope of the graph of the profit function taken from the origin to the maximum point of the graph
C. When the company produces 5,500 bicycles, x = 5.5, we have;
F(5.5) = 1.25 + 0.35 × 5.5 = 3.175
The cost is 3.75 × $100,000 = $375,000 and the profit from te graph is $300,000
Therefore, the cost of making the 5,500 bicycles is more than the profit made in sales
The company should plan on making fewer than 4,000 bicycles, to reduce cost of producing more bicycles and to increase profit per unit of bicycle sold