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[solved] hw 1)You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3...


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1)You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 400 eggs and 750 cups of cream. You make a profit of $3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha. How many quarts of each flavor should you make in order to earn the largest profit? HINT [See Example 2.] (If an answer does not exist, enter DNE.)

Creamy Vanilla????

?___________quarts

Continental Mocha????

__________ quarts

2)

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

?

Maximize p = x + y subject to

x+3y?8

3x+y?8

x ? 0, y ? 0.

p =

?(x,y) =(??? ,???? )

?

3)

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

?

Maximize p = x + 2y subject to

x+4y?16

2x+y?11

x ? 0, y ? 0.

p =

(x,y) = (????? ,??????? )

?

4)

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

?

Maximize p = 3x + y subject to

3x?8y?0

8x?3y?0

x+y?11

x ? 0, y ? 0.

p =

?(x, y) = (????????? ,??????? )

5)

?

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

?

Maximize p = x ? 2y subject to

x+2y?9

x?7y?0

7x?4y?0

x ? 0, y ? 0.

p =

?

(x, y) =(??? ,???? )

?

6)

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

?

Maximize p = 4x + 2y subject to

1.8x+0.9y?9

0.11x+0.22y?1.1

2x+2y?12

?

x ? 0, y ? 0.

p =

?

(x,y) = (???? ,?????? )

?

7)

?

The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 770 homeless patients and no more than 1,000 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,700 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,800 per month. How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.)

high-income patients???__________?

?

?

homeless patients????_____________

?

?

profit????$__________


1. Creamy Vanilla =150

 

Continental Mocha = 100

 

2. P=4

 

(x,y) =(2, 2)

 

3. P=10

 

(x,y) = (4, 3)

 

4. P=27

 

(x,y) = (8, 3)

 

5. P=5

 

(x, y) = (7, 1)

 

6. UNBOUNDED 7. High-income patients: 600

 

Homeless patients:...

 


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