Department of Management, UTSC
MGOC10 Analytics for Decision Making – L01/L02
Assignment #1 – Spring 2025
• Due by TUE May 13 at 11pm online, using the Assignment Tool in Quercus.
• You can do this assignment individually or in groups of 2 and does not have to be in the same section.
Please put both names/number/section on the assignment and submit one copy.
• You can write or type the assignment, it is your choice. Please submit a SINGLE Word, PDF or JPG file.
Problem 1
A baseball bat company makes two models, the “slugger” and the “whacker”. Each slugger requires 4
minutes of lathe work, and one minute of varnishing. Each whacker requires 5 minutes of lathe work and
45 seconds of varnishing. Each day, the combined production cannot exceed 1000 bats. The woodworking
shop operates 15 hours/day, with one room containing five lathes, and one varnishing room. Each of the
five lathes is available for 55 minutes each hour, and the varnishing room is available for 50 minutes each
hour. Each slugger contributes $5 to profit, and each whacker contributes $6.
(a) Formulate an LP model to determine how many sluggers and whackers should be made each
day to maximize profits. (hint: Since the variables are per day, you need to compute the resources
on a daily basis.) (6 marks)
(b) Solve the model using the graphical method presented in class. Clearly mark the feasible region.
How many sluggers and whackers are made each day and what is the profit? (10 marks)
(c) Are there any unused Lathe work or Varnishing hours? How many? (2 marks)
Problem 2
BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the
coming year. The advertising budget is $10,000,000. Because BP wants to push its new sodas, at least
one-half of the advertising budget is to be devoted to new soda advertising. However, at least $2,000,000
is to be spent on its traditional sodas. BP estimates that each dollar spent on traditional sodas will translate
into 100 cans sold, whereas, because of the harder sell needed for new products, each dollar spent on new
sodas will translate into 50 cans sold. To attract new customers, BP has lowered its profit margin on new
sodas to 2 cents per can as compared to 4 cents per can for traditional sodas.
(a) Formulate an LP model to help BP allocate its advertising budget if it wants to maximize its
profits while selling at least 750 million cans. (5 marks)
(b) Solve the model using the graphical method presented in class. Clearly mark the feasible region
and direction of increase/decrease of Z. How much money should BP invest in each soda and
what is the profit? (10 marks)
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