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Solve the linear programming problem.

Maximize P = 30x + 40y

Subject to 

1. What is the maximum value of P? Select the correct choice below and fill in any answer boxes present in your choice.

a) P=_____(Type an integer or a fraction.)

b) There is no maximum value of P.

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Jamar Ferry
Jamar FerryLv2
27 Apr 2020

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2. (20 pts) An object begins moving along a vertical line at time t = Os and stops at time t = 6 s. Its height above the ground at time t is given by h(t) in the provided graph, where h is measured in meters. Use the graph to answer the following questions. on 0 (a) Compute the average velocity of the object on the time interval [0,6). Show your work. N 1 2 3 4 5 6 (b) Circle the choice that best describes the shape of the graph on the time interval (5,6). i. increasing and concave up ii. increasing and concave down iii. decreasing and concave up iv. decreasing and concave down (c) At what time is the object farthest away from the ground? What is the velocity at that time? time= velocity= (d) The maximum velocity attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2 s iii. 3s iv. 4s v. 5s (e) Estimate the value of the maximum velocity attained. The value is an integer. (f) Let v(t) be the velocity at time t. Circle the greatest value amongst the following choices. i. v(2.5) ii. (2.6) ii. v(2.7) iv. v(2.8) V. (2.9) (8) List the time interval(s) on which the velocity is increasing. Use integer endpoints. (h) The maximum speed attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2s iii. 35 iv. 4s v. 5s

A food wholesaler has three kinds of individual bags of potato​ chips: regular,​ barbeque, and salt and vinegar. She wants to sell the bags of chips in bulk packages. The bronze package consists of 20 bags of regular and 10 bags of barbeque. The silver package contains 20 bags of​ regular, 10 bags of​ barbeque, and 10 bags of salt and vinegar. The gold package consists of 30 bags of​ regular, 10 bags of​ barbeque, and 10 bags of salt and vinegar. The profit is
​$10
on each bronze​ package,
​$30
on each silver​ package, and
​$50
on each gold package. The food wholesaler has a total of
8000
bags of regular​ chips,
3700
bags of​ barbeque, and
1600
bags of salt and vinegar. Assume all the packages will be sold. Use the simplex method to complete parts​ (a) and​ (b).
​(a) How many​ gold, silver, and bronze packages should be made up in order to maximize​ profit? What is the maximum​ profit?
 
Set up the linear programming problem. Let
x 1​,
x 2​,
and
x 3
represent the numbers of​ bronze, silver, and gold packages made​ up, respectively, and let z be the total profit.
 
 
Minimize
Maximize
zequalsnothing
subject to
20 x 1 plus 20 x 2 plus 30 x 3
 
less than
greater than
less than or equals
greater than or equals
nothing
 
10 x 1 plus 10 x 2 plus 10 x 3
 
greater than
greater than or equals
less than
less than or equals
nothing
 
10 x 2 plus 10 x 3
 
less than or equals
greater than
greater than or equals
less than
nothing
 
x 1greater than or equals​0,
x 2greater than or equals​0,
x 3greater than or equals0.
​(Do not factor. Do not include the​ $ symbol in your​ answers.)

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