Homework answers / question archive / Course Number & Title: MGT4310  Operations Management The General Store at State University is an auxiliary bookstore located near the dormitories that sells academic supplies, toiletries, sweatshirts and T-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks

Course Number & Title: MGT4310  Operations Management The General Store at State University is an auxiliary bookstore located near the dormitories that sells academic supplies, toiletries, sweatshirts and T-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks

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Course Number & Title: MGT4310  Operations Management

1. The General Store at State University is an auxiliary bookstore located near the dormitories that sells academic supplies, toiletries, sweatshirts and T-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks. The manager of the store has noticed that several pizza delivery services near campus make frequent deliveries. The manager is therefore considering selling pizza at the store. She could buy premade frozen pizzas and heat them in an oven. The cost of the oven and freezer would be $30,000. The frozen pizzas cost $4.5 each to buy from a distributor and to prepare (including labor and a box). To be competitive with the local delivery services, the manager believes she should sell the pizzas for $8.0 apiece. The manager needs to write up a proposal for the university’s director of auxiliary services.

1. Determine how many pizzas would have to be sold to break even.
2. If the General Store sells 40 pizzas per day, how many days would it take to break even?
3. The manager of the store anticipates that once the local pizza delivery services start losing business, they will react by cutting prices. If after a month (30 days) the manager has to lower the prices of a pizza to $7.2 to keep demand at 40 pizzas per day, as she expects, what will the new break-even point be, and how long will it take the store to break even?

 

2. A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18 ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The demand for bracelets is no more than four. A necklace earns $300 in profit and a bracelet, $400. The store wants to determine the number of necklaces and bracelets to make in order to maximize profit.
   1. Formulate a linear programming model for this problem. 
   2. Solve this model by using graphical analysis.
   3. Explain the effect on the optimal solution of increasing the profit on a bracelet from $400 to $600. What will be the effect of changing the platinum requirement for a necklace from 2 ounces to 3 ounces?

 

3. A linear programming model is given as follows:

 

Minimize       ?

 

Subject to         

                                     ?

                            

 

 

                                      

 

 

 

1. Define the feasible solution area and obtain the optimal solution graphically.
2. If the coefficient of ?

   

   in the objective function decreases to 4, what effect will be?
3. If the second constraint,

   

   , is removed from the given model, what effect will be?
4. If a new constraint, 4

   

   , is added to the given model, what effect will be?

 

 

 

4. A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping space for a maximum of 26 acres’ worth of strawberries and 37 acres’ worth of tomatoes. An acre of strawberries requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labor and 20 tons of fertilizer. The profit from an acre of strawberries is $400, and the profit from an acre of tomatoes is $300. The farmer wants to know the number of acres of strawberries and tomatoes to plant to maximize profit.

1. Formulate a linear programming model for this problem.
2. Identify all the possible extreme point solutions and solve the model, i.e., find the optimal solution, by using graphical analysis.

 

5.  The Valley Wine Company produces two kinds of wine—Valley Nectar and Valley Red. The wines are produced from 64 tons of grapes the company has acquired this season. A 1,000-gallon batch of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons. However, production is limited by the availability of only 50 cubic yards of storage space for aging and 120 hours of processing time. A batch of each type of wine requires 5 cubic yards of storage space. The processing time for a batch of Nectar is 15 hours, and the processing time for a batch of Red is 8 hours. Demand for each type of wine is limited to seven batches. The profit for a batch of Nectar is $9,000, and the profit for a batch of Red is $12,000. The company wants to determine the number of 1,000-gallon batches of Nectar and Red to produce in order to maximize profit. 

1. Formulate a linear programming model for this problem. 
2. Solve this model by using graphical analysis. 
3. How much processing time will be left unused at the optimal solution? 
4. What would be the effect on the optimal solution of increasing the available

storage space from 50 to 60 cubic yards?