Consider the following optimization problem:
min: x1+x2
subject to -4x1+ 4x2< =1
-8x1 +10x2> =15
x1, x2> =0
a. what is the optimal solution to the problem? round your answers to two decimal places, if necessary.
b. now suppose that x1 and x2 must be integers. what is the optimal solution?
c. what general principle of integer programming is illustrated by this question?

Ms. sophia jones, the company president, has heard that there are multiple breakeven points for every product. she does not believe this and has asked you to provide the evidence of such a possibility. some information about the company for 2017 is as follows:

The company financial officer was interested in the average cost of pcs that had been purchased in the past six months. she took a random sample of the price of 10 computers, with the following results. $3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000 what is the iqr?

In december of 2004, the company you own entered into a 20-year contract with a grain supplier for daily deliveries of grain to its hot dog bun manufacturing facility. the contract called for "10,000 pounds of grain" to be delivered to the facility at the price of $100,000 per day. until february 2017, the supplier provided processed grain which could easily be used in your manufacturing process. however, no longer wanting to absorb the cost of having the grain processed, the supplier began delivering whole grain. the supplier is arguing that the contract does not specify the type of grain that would be supplied and that it has not breached the contract. your company is arguing that the supplier has an onsite processing plant and processed grain was implicit to the terms of the contract. over the remaining term of the contract, reshipping and having the grain processed would cost your company approximately $10,000,000, opposed to a cost of around $1,000,000 to the supplier. after speaking with in-house counsel, it was estimated that litigation would cost the company several million dollars and last for years. weighing the costs of litigation, along with possible ambiguity in the contract, what are three options you could take to resolve the dispute? which would be the best option for your business and why?