HSA.CED.A.3 Tutor Intake — Constraints, Feasible Regions, and Viable Solutions

A company makes product A and product B. The following conditions apply:

• The total production time must be at most 120 hours (product A takes
  2 hours each; product B takes 3 hours each).
• The company must produce at least 15 units total.
• Product B production is capped at 40 units.
• Neither product can be produced in a negative quantity.

Let $a$ = units of product A and $b$ = units of product B. How many
constraints does this situation have in total (including non-negativity)?

Which boundary line convention is correct for the inequality
$2x + 4y \leq 30$?

A feasible region is defined by this system:

$10x + 5y \geq 40$
$2x + 4y \leq 30$
$x \geq 0$
$y \geq 0$

Substitute $(5, 5)$ into the protein constraint $10x + 5y \geq 40$.
What is the value of $10(5) + 5(5)$?

A meal-planning scenario has two foods: food A ($10\text{ g}$ protein/lb,
$\text{\char"0024}2$/lb) and food B ($5\text{ g}$ protein/lb, $\text{\char"0024}4$/lb). Let $x$ =
pounds of food A and $y$ = pounds of food B.

Constraints: the meal must provide at least 40 g of protein AND cost at
most $30.

Which system correctly models ALL constraints, including non-negativity?

A system of constraints for a manufacturing problem is:

$2a + 3b \leq 120$
$a + b \geq 15$
$b \leq 40$
$a \geq 0,\ b \geq 0$

Is the production plan $(a, b) = (50, 20)$ a viable solution?

For the constraint $a + b \geq 15$, evaluate the left side at the
production plan $(a, b) = (10, 10)$.

What is the value of $a + b$ at this point?