Project Statement: You have been hired to design a computer case. It will be a rectangular prism. The left side will be

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Project Statement: You have been hired to design a computercase. It will be a rectangular prism. The left side will be made ofglass and the top and right side will be made of metal. The backand front will be half consisting of a metal grate to allow airflow and half the same metal as is used on the right side. Thebottom will be made of a thicker metal. The volume of the case mustbe 1100 in3 . The manufacturer seeks the dimensions in inches thatminimize the total cost of manufacturing the case, given that thewidth of the front is desired to be 8 inches. The cost formaterials is as follows: Material Cost Glass $5/ft2 Metal for sides$15/ft2 Metal grate $20/ft2 Metal for bottom $20/ft2 Glue for seamof glass to metal $0.05/in Complete the following and show allwork. 1. State the function to be optimized, in terms of the widthand height of the sides, using the following as a guide. (a) Whatis the cost of manufacturing the left (glass) side? (b) What is thecost of manufacturing the top and right sides? (c) What is the costof manufacturing the back and front? (d) What is the cost ofmanufacturing the bottom? (e) What is the cost of gluing the glassto the metal on the right side? (f) What is the total cost ofproducing the case? 2. State the constraint equation, written interms of width and height. 3. Solve the constraint equation for onevariable. 4. Substitute the expression for that variable into thefunction to be optimized and simplify. 5. Find the first derivativeof the function. 6. Find the critical numbers. 7. Using the firstderivative test, determine if the critical number is the locationof the absolute minimum cost on the interval of interest. 8. Statethe dimensions of the case of minimum cost. Round to 2 decimalplaces and include units. 9. State the cost of manufacturing onecase. 10. Given that a standard motherboard is 12 in by 10 in, doesyour answer make sense?