#3: [35 pts] This problem is not a modeling problem. This problem is a Simplex Method solution problem. The scenario description is given here for context related to the final question. Scenario: A manufacturer of picture frames would like to find a profit-optimal production plan for this week's production schedule. The machinery is tooled for the production of any combination of three types of frames. Each type of frame requires a certain quantity of wood, glass panes and machine time. There are 320 hours of machine time, 200 feet of framing wood and 150 glass panes available. The profit and resource requirements for each type of frame are given in the following table.frame type profit machine time wood glass (8) (hours) (feet) (panes) 1 10 1 8 1 2 20 3 2 1 3 30 2 2 2 If we let xi be the number of frames of type 2' to manufacture and z be the expected profit in dollars, then the following LP can be used to determine the optimal production plan. max 2 = 101131 + 2Ozr2 + 305v3 S.t 1'1 + 1'2 + 2$3 S 8:131 + 25132 + 2$3 S x1 + 3302 + 213 S 320 as 2 0, at E R" (a) Formulate an equivalent standard form LP by the addition of three slack variables. (b) Solve this new LP using a Simplex tableau. Assume an initial basis given as the indices of the slack variables added in part Show / explain your steps and conclusions. (0) Provide an interpretation of all six decision variables in the context of the given manufacturing scenario. (d) For What profit values for type 1 frames (currently $10) does your solu- tion remain optimal