a carpenter earns $80 for the sale of a table, t, and $20 for the sale of a rocking chair, c. it takes 4…

a carpenter earns $80 for the sale of a table, t, and $20 for the sale of a rocking chair, c. it takes 4 hours for him to make a table and 5 hours to manufacture each rocking chair. he is limited to working at most 40 hours per week. the average manufacturing cost to the carpenter is $10 per table and $15 for every rocking chair. he wishes to keep his manufacturing costs to no more than $500 per week. given these various constraints, he wishes to maximize his revenue, r.\na) in each blank box below, select the best answer from the list that helps complete the objective function and its associated constraint inequalities. please note that the option <= indicates ≤, and the option >= indicates ≥.\nr = 20 c+ 80 t\n5c+ 4 t <= 40\n15 c + 10t <= 500\nb) use the geometric approach (with c placed on the x - axis and t on the y - axis) to determine the coordinates of the corner points of the solution region. then, select the answer from this list: select\nc) which of the corner points you selected in part (b) above maximizes the objective function? select the answer from this list: select\nd) what is the maximum revenue? select

a carpenter earns $80 for the sale of a table, t, and $20 for the sale of a rocking chair, c. it takes 4 hours for him to make a table and 5 hours to manufacture each rocking chair. he is limited to working at most 40 hours per week. the average manufacturing cost to the carpenter is $10 per table and $15 for every rocking chair. he wishes to keep his manufacturing costs to no more than $500 per week. given these various constraints, he wishes to maximize his revenue, r.\na) in each blank box below, select the best answer from the list that helps complete the objective function and its associated constraint inequalities. please note that the option <= indicates ≤, and the option >= indicates ≥.\nr = 20 c+ 80 t\n5c+ 4 t <= 40\n15 c + 10t <= 500\nb) use the geometric approach (with c placed on the x - axis and t on the y - axis) to determine the coordinates of the corner points of the solution region. then, select the answer from this list: select\nc) which of the corner points you selected in part (b) above maximizes the objective function? select the answer from this list: select\nd) what is the maximum revenue? select

Answer

Explanation:

Step1: Define objective function

Revenue ( R = 80T + 20C ) (80 per table ( T ), 20 per chair ( C ))

Step2: Time constraint

( 4T + 5C \leq 40 ) (4h/table, 5h/chair, max 40h)

Step3: Cost constraint

( 10T + 15C \leq 500 ) ($10/table, $15/chair, max $500)

Step4: Identify feasible region corners

Feasible region bounded by non-negativity and time (cost not binding). Corners: (0,0), (0,10), (8,0)

Step5: Calculate revenue at corners

  • (0,0): ( R=0 )
  • (0,10): ( R=80(10)+20(0)=800 )
  • (8,0): ( R=80(0)+20(8)=160 )

Step6: Determine maximum

Max revenue at (0,10) is 800

Answer:

a) 20, 80, 4, <=, 15, <= b) (0,0), (0,10), (8,0) c) (0,10) d) 800