Answer:
a) [tex]p \geq 60\,ft^{2}[/tex], b) [tex]w \geq 36\,ft[/tex], c) [tex]1\,qt \leq q \leq 2\,qt[/tex], d) [tex]0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65[/tex]
Step-by-step explanation:
In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:
a) At least 60 square feet of plywood for the surface
Let [tex]p[/tex] the surface area of plywood, measured in square feet, and the inequation is:
[tex]p \geq 60\,ft^{2}[/tex] (Eq. 1)
b) At least 36 feet of wood planks for the frame of the dog house
Let [tex]w[/tex] the total length of wood planks, measured in feet, and the inequation is:
[tex]w \geq 36\,ft[/tex] (Eq. 2)
c) Between 1 and 2 quarts of paint
Let [tex]q[/tex] the total capacity of paint, measured in quarts, and the inequation is:
[tex]1\,qt \leq q \leq 2\,qt[/tex] (Eq. 3)
d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.
Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let [tex]p[/tex], [tex]w[/tex] and [tex]q[/tex] the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:
[tex]0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65[/tex] (Eq. 4)
Write an inequality to represent each constraint(material and cost)
Plywood:
plywood ≥ 60 square feet
Planks:
planks ≥ 36 feet
Paints
1 quarts ≤ paints ≤ 2 quarts
Inequality to represent cost constraint
Plywood = $0.70
planks of wood = $0.10
paint costs $8
Total cost = $65
0.70 × p + 0.10 × pw + 8 × Pa ≤ 65
0.70p + 0.10pw + 8pa ≤ 65
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