Linear Programming problem: "Matt considers to start delivering food for Delivery guy, but he is worried that..."

[marvan]

Matt considers to start delivering food for Delivery guy, but he is worried that he might not be able to earn more money than it will cost to do deliveries.
There are three restaurants in his delivery radius where he can accept deliveries.

His average cost of delivering food is Chinese Food ($15), Fried Chicken ($7), and Pizza ($15).
The earnings for delivering food are Chinese Food ($25), Fried Chicken ($10), and Pizza ($12).

He can make an average of 36 deliveries every day.
Chinese Food deliveries take twice as long as the average delivery.
Fried chicken deliveries take one-quarter of the average delivery time.

Matt needs to make a minimum of $200 in daily profit.
He also needs to make at least 5 deliveries of each type each day to maintain his contract with Delivery guy.

a) Formulate and solve the problem as a Linear Programming problem to minimize cost.
b) Formulate and solve the problem as a Linear Programming problem to maximize profit.
c) What is the difference in profit between a) and b)? Explain why these changes occurred.

 

[stapel]

Matt considers to start delivering food for Delivery guy, but he is worried that he might not be able to earn more money than it will cost to do deliveries.
There are three restaurants in his delivery radius where he can accept deliveries.

His average cost of delivering food is Chinese Food ($15), Fried Chicken ($7), and Pizza ($15).
The earnings for delivering food are Chinese Food ($25), Fried Chicken ($10), and Pizza ($12).

He can make an average of 36 deliveries every day.
Chinese Food deliveries take twice as long as the average delivery.
Fried chicken deliveries take one-quarter of the average delivery time.

Matt needs to make a minimum of $200 in daily profit.
He also needs to make at least 5 deliveries of each type each day to maintain his contract with Delivery guy.

a) Formulate and solve the problem as a Linear Programming problem to minimize cost.
b) Formulate and solve the problem as a Linear Programming problem to maximize profit.
c) What is the difference in profit between a) and b)? Explain why these changes occurred.

Kindly please review the "Read Before Posting" thread, and then reply with the requested information, starting with the definitions for the variables you have chosen. Thank you!

Eliz.

 

[marvan]

Variables:

C = Chinese Food
F = Friend Chicken
P = Pizza

a) Minimize Z = C15 + F7 + P15
Not sure of the constraints?

b Maximize Z = C25 + F10 + P12
Not sure of the constraints.
Also not sure how to handle the problem in terms of the cost of delivery. Must it be subtracted?

Thanks for the help.

 

[khansaheb]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this problem

 

[stapel]

Variables:

C = Chinese Food
F = Friend Chicken
P = Pizza

When you say that "C = Chinese Food", are you referring to the delivery cost per order, the number of deliveries/orders, or something else?

a) Minimize Z = C15 + F7 + P15

When a number follows a variable, it is customarily an exponent, so "C15" usually means [imath]C^{15}[/imath]. I suspect that you actually mean [imath]15C[/imath]. Is that correct?

Not sure of the constraints?

Can he make a negative number of deliveries? Are all deliveries equal, or do some take more time/resources than do others? Can he make unlimited deliveries in a given day, or is there a limit?

b Maximize Z = C25 + F10 + P12

Same question as for (a).

Not sure of the constraints

Look at the stated limitations on what you're expected to optimize.

Also not sure how to handle the problem in terms of the cost of delivery. Must it be subtracted?

What is the definition of "profit"?

Eliz.

 

[khansaheb]

He can make an average of 36 deliveries every day.
Chinese Food deliveries take twice as long as the average delivery.
Fried chicken deliveries take one-quarter of the average delivery time.

How is average delivery time defined?

How is it (average delivery time) related to the "profit"?

 

[Steven G]

Variables:

C = Chinese Food
F = Friend Chicken
P = Pizza

You need to think about how you defined your variables. For example, if C=7, what does that mean? Chinese Food is not something numerical. How many grains of rice you get from the Chinese Food is a numerical value.