A craftsman builds two kinds of birdhouses, one for wrens (X1), and one for blue

Question

A craftsman builds two kinds of birdhouses, one for wrens (X1), and one for bluebirds 0X2). Each wren birdhouse takes four hours of labor and four units of lumber. Each bluebird house requires two hours of labor and twelve units of lumber. The craftsman has available 60 hours of labor and 120 units of lumber. Wren houses profit $6 each and bluebird houses profit $15 each. Use the Excel Solver output below to answer the following questions. 3. A. What is the optimal solution and the optimal value of the objective function (maximum profit)? B. Which constraints are binding and why? C. If the lumber availability comes down by 20 units, what is the new objective function value (profit)? (25 points) Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease 12 24 I$9 X2 12 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H.Side Increase Decrease 0.3 1.2 60 60 240 40 60

Explanation / Answer

a)
x1 = 12 , x2 = 6   {see final value column in first table}
optimal value of objective function
= 6 * 12 + 15 * 6
= 72 + 90
= 162
b)
both constraints are binding
as theire shadow price is non-zero
or
constraint R.H. side is same as Final value

c)
The Shadow Price of a binding constraint is the amount by which
value of the objective function cahnges if constraint changes by one unit
here
lumber has shadow price = 1.2
hence change = -20 * 1.2 = -24

new profit = 162 - 24
= 138

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