Question 1176641
Let's solve this linear programming problem step-by-step.

**1. Define Variables**

* Let 'x' be the number of ski pants.
* Let 'y' be the number of ski jackets.

**2. Formulate the Objective Function**

The objective is to maximize profit. The profit function (P) is:

* P = 2x + 1.5y

**3. Formulate the Constraints**

* **Sewing Time Constraint:** 8x + 4y ≤ 60
* **Cutter Time Constraint:** 4x + 8y ≤ 48
* **Non-negativity Constraints:** x ≥ 0, y ≥ 0

**4. Simplify the Constraints**

* **Sewing Time:** 2x + y ≤ 15
* **Cutter Time:** x + 2y ≤ 12

**5. Find the Corner Points**

* **Point 1 (Origin):** (0, 0)
* **Point 2 (x-intercept of sewing time):** Set y = 0 in 2x + y = 15. 2x = 15, x = 7.5. (7.5, 0)
* **Point 3 (y-intercept of cutter time):** Set x = 0 in x + 2y = 12. 2y = 12, y = 6. (0, 6)
* **Point 4 (Intersection of the two constraints):**

   Solve the system of equations:

   * 2x + y = 15
   * x + 2y = 12

   Multiply the second equation by 2:

   * 2x + 4y = 24

   Subtract the first equation from this:

   * 3y = 9
   * y = 3

   Substitute y = 3 into x + 2y = 12:

   * x + 6 = 12
   * x = 6

   Intersection point: (6, 3)

**6. Evaluate the Objective Function at Each Corner Point**

* **(0, 0):** P = 2(0) + 1.5(0) = 0
* **(7.5, 0):** P = 2(7.5) + 1.5(0) = 15
* **(0, 6):** P = 2(0) + 1.5(6) = 9
* **(6, 3):** P = 2(6) + 1.5(3) = 12 + 4.5 = 16.5

**7. Determine the Maximum Profit**

The maximum profit is $16.50, which occurs at the point (6, 3).

**Answers**

* **Pairs of pants:** 6
* **Jackets:** 3
* **Maximum profit:** $16.50