Apencil square prism (made from the macgun tree) with a capacity of 96in3 is to be constructed in the shape of a rectangular box with a square base and an open top. the material for all the sides costs 1.37$/in2and the material for the base costs 4.11$/in2. the marketing department has determined that the demand for these pencil square prisms is represented by the following function, where p denotes the cup's unit price (in dollars) and x denotes the quantity demanded. p=701.44−43.84x; (0≤x≤15)to get the most out of the tree we want to use the optimal dimensions of the square prism to reduces the cost for production. no matter how many square prisms, we expect to spend the same amount as the minimum cost to make (this means the cost function will be linear).the boss want to know a few thing about the production of at most 15 of the tree pencil square prisms.1. ignoring the completeness of the square prism, what is the interval for which the : (a) cost is increasing? (b) revenue is increasing? (c) profit is increasing? (d) cost is decreasing? (e) revenue is decreasing? (f) profit is decreasing? (2) ignoring the completeness of the square prism, what is the: (a) number of units to achieve maximum revenue? (b) most revenue that can be achieved? (c) number of units to achieve maximum profit? (d) most profit that can be achieved? (3) in this situation does the most revenue imply the most profit? (4) after how many units need to be sold before we start to loss a profit?