Let $P = \{(x, y) : x + 1 \geqslant y,\, x \geqslant -1,\, y \geqslant 2x\}$. Then the minimum value of $(x + y)$ where $(x, y)$ varies over the set $P$ is
(A) $-1$
(B) $-3$
(C) $3$
(D) $0$

A manufacturer produces two types of electric vehicles, Type A and Type B. The costs for producing these two types involve three categories: battery, motor, and others. The costs for each category are shown in the table below (unit: 10,000 yuan):

	Battery Cost	Motor Cost	Other Cost
Type A	56	26	48
Type B	40	20	56

The selling price formula for the two types of electric vehicles is the sum of ``$x$ times the battery cost'', ``$y$ times the motor cost'', and ``$\frac { x + y } { 2 }$ times the other cost'', that is,
Selling Price $=$ Battery Cost $\times x +$ Motor Cost $\times y +$ Other Cost $\times \frac { x + y } { 2 }$ where the multipliers $x, y$ must satisfy ``$1 \leq x \leq 2, 1 \leq y \leq 2$, and the selling prices of both Type A and Type B electric vehicles do not exceed 200 (10,000 yuan)''. To differentiate its products, the manufacturer wants to maximize the price difference between Type A and Type B electric vehicles. Based on the above information, answer the following questions.
(1) Write the selling prices of Type A and Type B electric vehicles (in terms of $x$ and $y$), and explain why ``the selling price of Type A electric vehicles is always higher than that of Type B electric vehicles''. (4 points)
(2) On a coordinate plane, draw the feasible region of $(x, y)$ satisfying the conditions in the problem, and shade the region with diagonal lines. (4 points)
(3) Find the values of multipliers $x$ and $y$ that maximize the price difference between Type A and Type B electric vehicles. What is the maximum price difference in units of 10,000 yuan? (6 points)

A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions: (I) Area A does not exceed 15 hectares. (II) The sum of area A and area B does not exceed 24 hectares. (III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A. Let area A be $x$ hectares and area B be $y$ hectares.
Which of the following options for the ordered pair $(x, y)$ satisfies the above three conditions? (Single choice)
(1) $(7,15)$
(2) $(12,13)$
(3) $(14,10)$
(4) $(15,4)$
(5) $(16,8)$

A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions: (I) Area A does not exceed 15 hectares. (II) The sum of area A and area B does not exceed 24 hectares. (III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A. Let area A be $x$ hectares and area B be $y$ hectares.
Express the three conditions set by the person for area A and area B as a system of linear inequalities in $x$ and $y$.

A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions: (I) Area A does not exceed 15 hectares. (II) The sum of area A and area B does not exceed 24 hectares. (III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A. Let area A be $x$ hectares and area B be $y$ hectares.
Given that when the farmland is harvested, fruit A yields a profit of 6 ten-thousand yuan per hectare and fruit B yields a profit of 7 ten-thousand yuan per hectare, find the maximum profit from planting both fruits in ten-thousand yuan. Show the calculation process in the solution area of the answer sheet, and draw the feasible region in the diagram area of the answer sheet, marking all vertices of the region and shading the region with diagonal lines.