# The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs….

The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs. The plant uses three main resources to make furniture – wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows. The furniture is produced on a weekly basis and stored in the warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture. Each sofa earns \$300 in profit, each table \$200, and each chair \$150. The company wants to know how many pieces of each type of furniture to make per week to maximize profit. The worksheet named “Hickory 1” contains a template for solving this LP problem. Answer the parts below, and then use the LP template to solve for the maximum profit. (6 points) Be sure to choose “Simplex LP” and check the “Make Unconstrained Variables Non-Negative” box. a. 1 Point: In cell B3, use the Excel’s built-in function named “SUMPRODUCT” to write a formula for the objective function. Be sure to reference the appropriate cells. b. 3 Points: In cells B9:D9, enter the profit coefficients for the objective function. c. 6 Points: In cells B12:D15, enter the constraint coefficients for each of the four constraints. d. 2 Points: In cells E12:E15, enter the appropriate constraint values. e. 4 Points: In cells F12:F15, use the “SUMPRODUCT” function to write a formula for the amount of each resource used or limitation imposed. Be sure to reference the appropriate cells. f. 4 Points: In cells G12:G15, write the appropriate formulas to determine the amount of slack or surplus associated with each resource or limitation. g. 2 Points: In cells H12:H15, write the type of inequality associated with each constraint using either “<=,” “>=,” or “=.” h. 2 Points: In cells I12:I15, write the appropriate word (either “Slack” or “Surplus”) to indicate the nature of the leftover resources or limitations.

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