If A is a 5x4 matrix, and B is a 4x5 matrix, then AB is a 0 4x5 matrix 0 5x4 matrix 0 5x5 matrix 0 4x4 matrix \fThis question requires you to upload your work. Solve the linear programming problem by following the steps: (i) Graph the set of inequalities (use graph paper or a ruler to make the graph as precise as possible). (ii) Find the vertices of the feasible region. (iii) Evaluate the objective function at the vertices. (iv) State the optimal objective function value and the vertex at which the optimal value is obtained. Maximize 7x + 5y Subject to 2x+y58 x+y56 \fSet up the following linear programming problem (do not solve it): Moonshine Nucky is trying to give back to the community. He plans to establish a Food & Roof Foundation to help the less fortunate. Building the Foundation's main building requires 500 tons of timber and 900 tons of stone. Two companies in the area supply timber and stone. Company A charges $5/ton for timber and $4/ton for stone and a minimum of 200 tons of material must be ordered. Company B charges $6/ton for timber and $2/ton for stone and a minimum of 250 tons of material must be ordered. How many tons of timber and how many tons of stone must Nucky order from each company to minimize the total material cost