In the next 5 days you need to fly a total of 100 large boxes from England to Iceland. Based on deals in place and

In the next $5$ days you need to fly a total of $\mathrm{100}$ large boxes from England to Iceland.

Based on deals in place and the capacity of available aircrafts, the price and the maximum number

of boxes you can send over on each day differs as shown in the table below:

Day Price per box Maximum number of boxes

that can be shipped

Monday $\mathrm{Â\pounds }\mathrm{50}\mathrm{40}$

Tuesday $\mathrm{Â\pounds }\mathrm{60}\mathrm{50}$

Wednesday $\mathrm{Â\pounds }\mathrm{35}\mathrm{30}$

Thursday $\mathrm{Â\pounds }\mathrm{45}\mathrm{50}$

Friday $\mathrm{Â\pounds }\mathrm{50}\mathrm{50}$

The company in Iceland will pick up the boxes at the end of Friday. Any boxes sent over earlier would

need to be kept in storage at a cost of $\mathrm{Â\pounds }5$ per box per night.

Your goal is to find a schedule to transfer all $\mathrm{100}$ boxes to Iceland at a minimum total cost, including

transportation and storage.

Answer the following questions:

$\mathrm{1.}$ Formulate the problem above as an integer linear program: define decision variables and mention what each of them represents, formulate and explain the objective function and all necessary constraints.

$\mathrm{2.}$ Use LPSolve to solve the problem and write down the solution.