Question

question 11 of 40
a woodworking artist makes two types of carvings: type x and type y. he spends 3 hours making each type x carving and 2 hours making each type y carving, and he can spend up to 36 hours each week making carvings. his materials cost him $4 for each type x carving and $5 for each type y carving, and he must keep his weekly cost for materials to $100 or less. if x is the number of type x carvings he makes in a week and y is the number of type y carvings he makes in a week, which of the following systems of inequalities models this situation?

a. $3x + 2y \geq 36$, $4x + 5y \leq 100$

b. $3x + 2y \leq 36$, $4x + 5y \leq 100$

c. $3x + 2y \geq 36$, $4x + 5y \geq 100$

d. $3x + 2y \leq 36$, $4x + 5y \geq 100$

Explanation:

Step1: Analyze time constraint

Total hours ≤ 36: $3x + 2y ≤ 36$

Step2: Analyze cost constraint

Total cost ≤ 100: $4x + 5y ≤ 100$

Answer:

B. $3x + 2y ≤ 36$, $4x + 5y ≤ 100$