Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows. Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2 The sharper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contribution for components 1, 2, and 3 are $8, $6, and $9 respectively. Let x1 = the number of units of component 1 manufactured, x2 = the number of units of component 2 manufactured, and x3 = the number of units of component 3 manufactured. The MS Excel Worksheet is attached. Thoughtfully and carefully answer each of the questions below using the Excel output to justify your answers. Use the template on page three to help frame your response. A. Formulate the linear program for the recommended production quantities using the decision variable definitions above. B. Suppose that the objective coefficient associated with x1 is decreased by 4 units. Explicitly determine the impact this has on the optimal solution (i.e., the decision variable values and the objective function). Use the template on page three to structure your answer. C. Does the lower limit for the objective function coefficient of x1 make sense given the context of the problem? Thoroughly explain your answer. D. Suppose that the right hand side of constraint 6 decreases by 2 units. Explicitly determine the impact of this on the optimal z-value. Show your calculation. Use the template on page three to structure your answer. E. If more units of component 2 can be sold by reducing the sales price by $ 2, should the company reduce the price? Your answer needs to be thorough and convincing.