PROBLEM 6 (Lesson 9 Linear Programming) Computer Productions produces three keyboards: Regular, Special and Collector. The following cost data is available: Regular Special Collector SALES price per unit $310 $460 $550 Direct Variable manufacturing costs $110 $210 $250 Indirect Variable manufacturing costs $20 $30 $30 Fixed Manufacturing costs $50 $50 $50 GROSS MARGIN per unit $130 $170 $220 Marketing costs per unit $10 $ 10 $15 Distribution costs per unit $5 $5 $5 PROFIT per unit $115 $155 $200 Computer Productions fixed manufacturing costs are $20,000 per month. Based on an estimated monthly production of 400 units, they have assigned $50 of fixed costs per unit to cach keyboard produced, regardless of the type of keyboard. The marketing and distribution is fully outsourced to another company and Computer Productions has agreed on a price per unit for both marketing and distribution. The maximum demand for Regular keyboards is 250 units per month. The maximum demand for Special keyboards is 30 units per month. Computer Productions want to keep the Collector keyboard sales down to keep it a collector's item. Therefore the sales can be no more than 50% of the Regular keyboard sales. (Hint: You must create a constraint for this condition). Direct manufacturing labor hours are limited to 10,500 hours per month. Machine hours are limited to 5,100 hours per month. The Regular keyboard requires 20 hours of labor and 8 machine hours. The Special keyboard requires 34 hours of labor and 25 machine hours. The Collector keyboard requires 37 hours of labor and 22 machine hours. Management desires a product mix that will maximize the contribution margin towards fixed costs and profits given the constraints. Where: R=Regular keyboards S = Special keyboards C Collector keyboards REQUIRED: a) Formulate the correct set of equations (maximization formula and constraints) for the keyboard production process. b) Through Solver, generate the Answer Report. Use integers within your constraints. What is the volume of Regular, Special and Collector keyboards that will be produced? What is the total contribution margin? c) You have an opportunity to purchase a used machine for $15,000. This machine will last one year and allow you to increase your monthly machine hours to 5,450 hours. Should you purchase this machine? What is the overall gain for Computer Productions?