You have been hired to design a PC case. It will be a rectangular prism. The left side will be made of glass and the top and right side will be made of metal. The back and front will be half consisting of a metal grate to allow air flow and half the same metal as is used on the right side. The bottom will be made of a thicker metal. The volume of the case must be 1100 in ³. The manufacturer seeks the dimensions in inches that minimize the total cost of manufacturing the case, given that the width of the front is desired to be 8 inches. use rules of optimization Material Cost Glass $5/ft² Metal for sides $15/ft² Metal grate $20/ft² Metal for bottom $20/ft² Glue for seam of glass to metal $0.05/in a. State the constraint equation, written in terms of width and height. b. Solve the constraint equation for one variable. c. Substitute the expression for that variable into the function to be optimized and simplify. d. Find the first derivative of the function

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