Custom Office Furniture Company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three different models-A, B, and C-are to be marketed. Each model A desk requires hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model B desk requires hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model C desk requires hr, hr, and hr for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $26, the profit on each model B desk is $28, and the profit on each model C desk is $24. The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is 240 hr, 160 hr, and 150 hr, respectively. To maximize Custom's profit, how many desks of each model should be made in the month?
A) Maximize P = 26x + 28y + 24z subject to
B) Minimize P = 26x + 28y + 24z subject to
C) Maximize P = 26x + 28y + 24z subject to
D) Minimize P = 26x + 28y + 24z subject to
E) Minimize P = 26x + 28y + 24z subject to

Question

Custom Office Furniture Company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three different models-A, B, and C-are to be marketed. Each model A desk requires  hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model B desk requires  hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model C desk requires  hr,  hr, and  hr for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $26, the profit on each model B desk is $28, and the profit on each model C desk is $24. The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is 240 hr, 160 hr, and 150 hr, respectively. To maximize Custom's profit, how many desks of each model should be made in the month?
A) Maximize P = 26x + 28y + 24z subject to 
B) Minimize P = 26x + 28y + 24z subject to 
C) Maximize P = 26x + 28y + 24z subject to 
D) Minimize P = 26x + 28y + 24z subject to 
E) Minimize P = 26x + 28y + 24z subject to

Quizplus · Accepted Answer

We need to maximize the profit P, and there are three decision variables, namely x (number of model A desks), y (number of model B desks), and z (number of model C desks). The objective function is P = 26x + 28y + 24z.
The constraints come from the available time in each department. In the fabrication department, the total time required for the desks must be less than or equal to the available time of 240 hr: 
11eab448_e840_3b8d_acdb_71e821c673bb_TB6027_11. 
Similarly, in the assembly department, the total time must be less than or equal to the available time of 160 hr: 
11eab448_e840_3b8e_acdb_23b7b4f0a66a_TB6027_11. 
In the finishing department, the total time must be less than or equal to the available time of 150 hr: 
11eab448_e840_3b8f_acdb_150877802214_TB6027_11 + 11eab448_e840_3b90_acdb_e350b696911f_TB6027_11 + 11eab448_e840_3b91_acdb_6b2f631e091f_TB6027_11. 
Thus, the problem can be formulated as the following linear programming problem:

Maximize P = 26x + 28y + 24z 
subject to 
11eab448_e840_3b8d_acdb_71e821c673bb_TB6027_11
11eab448_e840_3b8e_acdb_23b7b4f0a66a_TB6027_11
11eab448_e840_3b8f_acdb_150877802214_TB6027_11 + 11eab448_e840_3b90_acdb_e350b696911f_TB6027_11 + 11eab448_e840_3b91_acdb_6b2f631e091f_TB6027_11
x >= 0, y >= 0, z >= 0

Solving this LP problem, we get x = 6, y = 0, and z = 5, which means Custom should produce 6 model A desks and 5 model C desks to maximize the profit, with no model B desks being produced.

Custom Office Furniture Company Is Introducing a New Line of Executive