David Co will manufacturers dining sets:

Product

Table

Chair

Sideboard

Direct Material (Wood panel)

32 sq ft/unit

6 sq ft/unit

44 sq ft/unit

Direct Labor

2.5 hours/unit

0.5 hours/unit

4 hours/unit

Gross Profit

$210/unit

$45/unit

$350/unit

There is a total of 800 direct labor hours available per week and 10,000 sq ft of Direct Material available per week. The company needs to produce a minimum of 20 large sets per week (each large set includes: 1 table, 8 chairs, and 2 sideboards) and 50 small sets (each small set includes: 1 table, 6 chairs, and 1 sideboard). The number of chairs produced has to be at least 6 per table and cannot exceed 8 per table. The number of sideboards has to be at least 1 per table and cannot exceed 2 per table. How many tables, chairs, and sideboards should the firm produce per week in order to maximize gross profit?

On a piece of paper, formulate the mathematical model (objective function and constraints).

How many variables did you find in this problem and what are their units?

Question 1 options:

3 variables: Tables (in $), Chairs (in $), Sideboards (in $)

3 variables: Tables (in units), Chairs (in units), Sideboards (in units)

2 variables: Direct Labor (in hours), Direct Materials (in Sq Ft)

7 variables: Tables (in $), Chairs (in $), Sideboards (in $), Direct Labor (in hours), Direct Materials (in Sq Ft), Large Sets (in units), Small Sets (in units)

Excluding the non-negative constraint, how many constraints did you find?

Question 2 options:

5

7

9

11

How many constraints have the sign "<="

Question 3 options:

2

4

6

8

Which of the following constraints is INCORRECT?

Question 4 options:

T>=70

C+6T >= 0

C>=460

C-8T <= 0

Which of the following is the Objective Function?

Question 5 options:

Max 32T + 6C + 44S

Max 10,000*DM + 20*LS + 50*SS

Max 210T + 45C + 350S

Max 2.5T + 0.5C + 4S

Consider the following formulation:

Max 2x + 4y

S.T.:

6x + 2y <= 20

x>=1

x+y<=4

x, y >= 0

On a piece of paper or on Desmos.com, solve the problem graphically.

How many extreme points did you find?

Question 6 options:

3

4

5

6

What is the optimal solution if the objective is to maximize profit?

Question 7 options:

(x=2.5 , y=1)

(x=1 , y=0)

(x=1 , y=3)

none of the above

Question 8(0.07875 points)

What is the optimal solution if the objective is to minimize cost?

(x=2.5 , y=1)

(x=1 , y=0)

(x=1 , y=3)

none of the above