Han wants to build a dog house. He makes a list of the materials needed: At least 60 square feet of plywood for the surfaces

At least 36 feet of wood planks for the frame of the dog house 

Between 1 and 2 quarts of paint

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.
write inequalities to represent the material constraints and cost constraints in this situation.

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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a) , b) , c) , d)

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 the surface area of plywood, measured in square feet, and the inequation is:

(Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let the total length of wood planks, measured in feet, and the inequation is:

(Eq. 2)

c) Between 1 and 2 quarts of paint

Let the total capacity of paint, measured in quarts, and the inequation is:

(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 , and 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:

(Eq. 4)

rounding to the nearest thousandth would be 452,000