A manufacturing company produces two types of gaming consoles, the Magic box and the Joy box consoles. The manufacturing process consists of two principal departments: design and production. The design department has $2100$ hours available each week, and the production department has $2000$ hours available each week. On average, to produce a Magic box, the company requires $3$ labor hours for design and $4$ labor hours for production. The Joy box requires $3$ labor hours for design and $2$ labor hours in production. The company makes a net profit of $$170$ on the Magic box, and $$150$ on the Joy box. The management of the company wants to determine how many of each console type should be produced on a weekly basis to maximize net profit.

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Flag question: Question $1$

Question $15$ pts

Which of the following is a decision variable in the given problem?

Group of answer choices

the labor hours required to produce the two types of consoles

total profit that the company wants to maximize

Joy box gaming consoles produced per week

the number of workers the firm has

Flag question: Question $2$

Question $25$ pts

If the numbers of Magic box and Joy box gaming consoles produced each week are denoted as X$1$ and X$2$ respectively, what is the objective function?

Group of answer choices

Max $130$X$1+150$X$2$

Min $170$X$1+150$X$2$

Max $170$X$1+150$X$2$

Min $130$X$1+150$X$2$

Flag question: Question $3$

Question $35$ pts

If the numbers of Magic box and Joy box gaming consoles produced each week are denoted as X$1$ and X$2$ respectively, the function that describes the design department's labor constraint for a week is $\_\_\_\_\_\_\_\_.$

Group of answer choices

$3$X$1+4$X$2>=2030$

$3$X$1+4$X$2<=2100$

$16$X$1+14$X$2>=8120$

$3$X$1+3$X$2<=2100$

Flag question: Question $4$

Question $45$ pts

If the number of Magic box and Joy box gaming consoles manufactured by the company in a week are $100$ and $150$ respectively, the number hours used in the design department is $\_\_\_\_\_\_\_\_.$

Group of answer choices

$850$

$900$

$750$

$500$

Flag question: Question $5$

Question $55$ pts

If the number of Magic box and Joy box gaming consoles manufactured by the company in a week are $100$ and $150$ units respectively, determine the total profit generated by the company in a week.

Group of answer choices

$$39,500$

$$90,000$

$$54,500$

$$35,500$

Flag question: Question $6$

Question $65$ pts

Using Solver, what is the optimum number of Magic box consoles to be manufactured each week?

Group of answer choices

$375$

$300$

$175$

$150$

Flag question: Question $7$

Question $75$ pts

Using Solver, what is the optimum number of Joy box consoles to be manufactured each week?

Group of answer choices

$375$

$350$

$175$

$400$

Flag question: Question $8$

Question $85$ pts

Using Solver, what is the maximum profit that the company can have using the current resources?

Group of answer choices

$$95400$

The company can produce infinite number of consoles and have infinite profit

$$111000$

$$75250$

Flag question: Question $9$

Question $90$ pts

Please upload your Excel file to get the points for Questions $6,7,$ and $8.$