Math - Linear Inequalities

The Wellbuilt Company produces two types of wood chippers, Deluxe and Economy.
The Deluxe model requires 3 hours to assemble and ½ hour to paint, and the Economy
model requires 2 hours to assemble and 1 hour to paint. The maximum number of
assembly hours available is 24 per day and the maximum number of painting hours
available is 8 per day. If the profit on the Deluxe model is $15 per unit and the profit on
the Economy model is $12 per unit, how many units of each model will maximize profit?
Let x = number of Deluxe models
y = number of Economy models
a. List the constraints
b. Determine the objective function. __________________
c. Graph the set of constraints. Place number of Deluxe models on the horizontal axis
and number of Economy models on the vertical axis.
d. Find the vertices of the feasible region.
Vertices Profit
e. How many Deluxe models and how many Economy models should the Wellbuilt
Company produce to maximize their profit?
Deluxe____________
Economy__________
f. What is the maximum profit? __________________

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  1. Using your definitions:

    3x+2y ≤ 24 (assembly restraint) and
    .5x+y ≤ 8 (painting restraint), alos
    x ≥ 0 and y ≥ 0

    Profit = 15x+12y

    Solving the two corresponding equations above gave me (4,6)

    so the vertices of your feasible region would be (0,0) (don't make any at all, silly)
    (0,8) and (16,0)

    "Sliding" the profit equation P=15x+12y, which has a slope of -5/4 away from the origin, while maintaining the slope would reach the point (4,6) of your region.

    Can you tie all this together, and reach the correct answers?

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  2. Ok I understand the constratints, Can you please explain me how you got feasible region (0,0), (0,8) and (16,0).

    And also slope -5/4.

    Thanks for your help

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