A furniture manufacturer makes a mix of desks (D) and chairs (C). Each desk uses two units of wood, and each chair uses four units of wood. Each desk generates a profit of $55, and each chair generates $35 in profit. Production facilities are setup in such a way that the number of chairs produced must be exactly 1.25 times the number of desks. The plant capacity is 40 pieces of furniture a day. There are 140 units of wood available per day. The furniture manufacturer wishes to find the optimal daily production combination of desks and chairs in order to maximize profit in a given day.
a. State the Objective function mathematically.
b. State the constraints mathematically.
c. Setup the model in Excel and use Solver to determine the optimized solution.
d. How many desks should be produced?
e. How many chairs should be produced?
f. What is the overall daily profit?
Note that Excel formulas and Solver settings need to be correct in Microsoft Excel in order to have an opportunity for full credit on this problem (even if the correct answers are shown). In addition, the Instructor will be running Solver on your spreadsheets to ensure the optimal solution is obtained, based on your model. Note: there is no need to specify optimized results to be integer values.