. Your baker has fivehours to make as many of each product before the store opens for the day. Inventory shows you have 60
pounds of flour and 25 pounds of sugar available. The cost per pound of flour is $1.00 and $2.00 per pound of sugar. It takes your baker 10 minutes to produce a dozen donuts and 12 minutes to produce a dozen bagels. The baker needs 2 pounds of flour and 1 pound of sugar to produce a dozen donuts and 3 pounds of flour for a dozen bagels, no sugar for the bagels. On average your customers consume at least 3times as many donuts as bagels but you still need at least 4 dozen bagelsper day to keep up with demand. You sell donuts for $7.00 per dozen and your bagels for $12.00 per dozen. How many dozen donuts and bagels should you produce to maximize profits?
a) [4 points] Formulate the model and write in standard form.Don’t forget to define your decision variables.
b) [6 points] Graphically solve the problem, find and label the feasible region and the optimal solution including the coordinates for X1 and X2.Turn in your graph using graph paper. (Don’t forget to label axis and your constraints with direction arrows and any objective function Z values you choose as a dashed line.) Show your slack/surplus amounts for each constraint and label the binding constraints.
c) [4 points] Solve the problem using the Management Scientist software and print out the solution. Put the computer output solution on one page and attach it to this page with your graphical solution. Check to see that the computer results match your graphical solution.
d) [3 points] While inventorying the flour, the baker notices that one 20 pound bag of flour has passed the expiration date and can’t be used. There is not enough time to replace the bag so he only has 40 pounds of flour available. What would be the new Objective FunctionValue (OFV) with only 40 pounds of flour? Show your work without resolving the computer problem.
e) [3 points] If you had a sale on bagels and lowered the price of the bagels to $8.00 per dozen. How much less total profit would you make? Show your work without resolving the computer problem.
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