A certain academic department at a local university will conduct a research proj

Question

A certain academic department at a local university will conduct a research project. The department will need to hire graduate research assistants and professional researchers. Each graduate research assistant will need to work 28 hours per week on fieldwork and 12 hours per week at the university's research center. Each professional researcher will need to work 12 hours per week on fieldwork and 28 hours per week at the university's research center. The minimum number of hours needed per week for fieldwork is 169 and the minimum number of hours needed per week at the research center is 138. Each research assistant will be paid $252 per week and each professional researcher will be paid $436 per week. Let x denote the number of graduate research assistants hired and let y denote the number of professional researcher hired. The department wants to minimize cost. Set up the Linear Programming Problem for this situation.

a) Min C = 252x + 436y  s.t. 28x + 12y> 169 , 28x + 12y> 138 , x> 0 , y> 0

b) Min C = 252x + 436y  s.t. 12x + 169y< 138 , 28x + 12y< 169 , x> 0 , y> 0

c) Min C = 252x + 436y  s.t. 28x + 12y> 169 , 12x + 28y> 138 , x> 0 , y> 0

d) Min C = 436x + 252y  s.t. 12x + 28y> 169 , 28x + 12y> 138 , x> 0 , y> 0

e) Min C = 436x + 252y  s.t. 28x + 12y> 169 , 12x + 28y> 138 , x> 0 , y> 0

f) None of the above.

Given the linear programming problem

Minimize C = x + 10y subject to
x< 2
y< 10
x + y> 10
x> 0, y> 0

Use the method of corners to determine the where the minimum occurs, and give the minimum value.

a) ( 0 , 10 ) with C = 100

b) ( 0 , 0 ) with C = 0

c) ( 2 , 0 ) with C = 2

d) ( 2 , 10 ) with C = 102

e) ( 2 , 8 ) with C = 82

f) None of the above.

John got a part time weekend job at a local restaurant to save for a new car. He plans on depositing $200 per month for the next 2 years in a savings account with a rate of 5% per year compounded monthly. How much will he have saved toward his down payment at the end of the 2 year period?

a) $4,997.18

b) $5,077.18

c) $5,007.18

d) $5,027.18

e) $5,037.18

f) None of the above.

You borrowed $11,000 from your bank to build a small cabin on your property. The bank will charge 6% per year compounded quarterly. You decide to pay off this loan in 2 years by making quarterly payments. How much are your quarterly payments?

a) $1,479.42

b) $1,449.42

c) $1,469.42

d) $1,499.42

e) $1,439.42

f) None of the above.

The manager of a manufacturing company knows that they will need a new machine in one of their factories. The new machine will cost them $12,500. The manager has determined that they can afford to pay 10% of the cost of the machine in cash. They can then finance the rest through a credit union. The credit union will charge 2% per year compounded monthly. How much are their monthly payments for 4 years?

a) $317.03

b) $244.07

c) $225.32

d) $250.36

e) $271.19

f) None of the above.

a) 131

b) 134

c) 135

d) 133

e) 129

f) None of the above.

Explanation / Answer

Since you posted multiple questions,i would be attaching answers for first one,can you please post rest of questions one at a time.

Let number of research assisstant =x
and number of professional researcher =y

so Each research assistant will be paid $252 per week and each professional researcher will be paid $436 per week

So total cost =252*x +436*y =252x +436y

Min C =252x +436y

Constraints:
For fieldwork, research assisstant need to work for 28 hours and professional researchers need to work for 12 hours. numbers of hours need at fieldwork are 169

so 28x +12y 169

For reserach center
research assisstant need to work for 12 hours and professional researchers need to work for 28 hours. numbers of hours need at research center are 138
So 12x+28y 138

also, x0 ,y0

so its choice C

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