4: Suppose that you have been put in charge of managing the clothing supply for a small, newly established space colony. The colony has n colonists each of whom needs at

least two pairs of shoes, three jumpsuits, and a hat. You can make each of these products from some combination of cotton, thread, and glue, all of which you need to import. You can also import already made clothing for a fixed cost. For each item that you produce in the factory, you also incur a cost of d per item (a pair of shoes, jumpsuit, and hat each count as an 'item') for the use of electricity in your factory. Write down (but do not solve) a linear program to minimize the cost of acquiring all of the clothing which your colony requires. You may assume that you are allowed to make and import fractional quantities of each of these goods. (20 pts)