Question

2. Alice opened two food factories, delivering lunch to students in USC and UCLA. One factory is located at Westwood, and another at Koreatown. Each factory can deliver at most 50 lunchboxes every day. The table below summarizes the profit of a lunchbo:x per student from two factories to two universities. USC UCLA Westwood 3.5$5 Koreatown $5.5 $2 Alice wants to know how to deliver lunch from two factorics according to the number of (i) On a day during the winter break, there are 10 orders from USC and 25 orders from (i) On a regular day in the quarter, there are 60 orders from USC and 40 orders from orders o OUSC and OOLA. Can you nelp ner using linear programmin8 UCLA. What's the best plan of delivery? UCLA, what's the best plan of delivery? i) On a day during the final week, there are 80 orders from USC and 60 orders from UCLA. So not every student can get the lunchbox. Those who don't get the lunchbox become angry, and will probably not order food from Alice's factories. A student from USC who does not get the lunchbox accounts for a loss of $1, and that from UCLA for a loss of S0.5. What's the best plan of delivery?

Answer 1

In the given problem, We will use the excel solver to find the profit maximization.

We will enter the data into excel. Raw data sheet will be as shown below -

Formula applied is mentioned in Table.

Here our objective will be to maximize the profit.

Variable cells will be D10:E11.

And Constraints will be sum of orders from UCS and UCLA should be equal to Demand.

Solver will look as mentioned below -

Final Result will be as mentioned below -

ii)

In this problem we will add one more constraints. It will that Total Delivered units will be less that or equal to Max available capacity of each factory. All the other processes will be same.

Final Result will be as mentioned below -

iii)

In this problem, order from each locations are greater than 50. Hence we will calculate the optimal solution from each location with 50 orders and delivery more than 100 will not be possible. Result will be as mentioned below -

From above, it is clear that 30 orders from USC and 10 orders from UCLA will not be get delivered.

Total Loss = 30*1 + 10*0.5 = $35