Question

A&F Hardware Inc. manufactures hammers and shovels from steel and wood using both skilled and unskilled labor. The following table gives the profit generated per unit, as well as the amount of wood, steel, skilled labor and unskilled labor required, per unit of each product along with their maximum monthly limits in terms of availability.

	Hammers	Shovels	Max Monthly Limit
Profit	$9.59 per unit	$12.6 per unit
Wood Required	$1.55 ft. per unit	$3.15 ft per unit	2000 feet
Steel required	1.85 lbs per unit	4.15 lbs per unit	2000 lbs
Total Skilled Labor	16 minutes per unit	12 minutes per unit	13800 minutes

total unskilled labor

6 minutes per unit

8 minutes per unit

6600 per unit

Given that A&F Hardware Inc. wants to earn the highest possible profits without violating these constraints, help the company decide how many hammers and shovels to produce by answering the following questions:

a) Clearly list down the decision variables, the objective function and the constraints in words. You will be marked for the clarity of your definition of these parameters as well the use of the standard verbal (Step 1) format for these parameters outlined in your textbook (and in class).

b) Clearly provide the mathematical expressions, equations and inequalities for the objective function and the constraints in the summary (Step 2) format prescribed in your textbook (and in class).

c) Formulate the mathematical linear programming model for this problem using Microsoft Excel and use Microsoft Excel Solver Add-in to solve the problem. You will be marked for clarity of formatting and labelling and using the Excel setup correctly.

d) How many of each type of product do you recommend A&F Hardware Inc. should produce per month to earn the highest possible level of profit without violating any constraints outlined above?

e) What would be the profit at this level?

Answer 1

(c).

(d). 753 hammers and 146 shovels should be produced

(e). Profit = $9060.87