The Dava family owns a durian farm at the far end of Holay village. In that village their family owns 5 hectares of durian trees which produce 2 tonnes of durian (unpeeled) per hectare annually. The family uses all of their durian harvest to produce durian cakes, durian eclairs, peeled durians and unpeeled durians in the local town. Sponges are sold for IDR 100,000 per unit, a box of 12 durian eclairs is sold for IDR 50,000, peeled durians are sold for IDR 120,000 per pack (1 pack contains about 2kg of durian), and non-peeled durians are sold for IDR 40,000 per kg . Peeled durians weigh half as much as unpeeled (non-peeled) durians. To make durian cakes, you need 4 ounces of peeled durian, and to make delicious durian eclairs, you need 6 ounces of peeled durian. The eclairs and durian cakes require an oven as a toaster so they taste more delicious and are worth selling. The available baking time for the use of the tool is 120 hours. It took 55 minutes to bake four units of sponge cake and it took 15 minutes to bake 24 units of durian eclairs. Packaging requires time from workers to research the operations of all products from the Dava family. It takes 10 minutes to peel durians and wrap them in packets for sale. It takes 1 minute to prepare unpeeled durians for sale. It takes 6 minutes to prepare durian cake wrappers and 4 minutes to wrap one dozen durian eclairs. They have a total of 300 man hours on the packaging. The Dava family asks you, as a friend of Dava Dava's operations, to calculate how many durian cakes, durian eclairs, peeled durians and non-peeled durians must be prepared and sold in order to research the operation for maximum profit!
a. From this case, formulate a linear equation model to solve the problem!

Next, solve the linear function in the general case above (may be with a solver, graph or other methods); then answer the following questions:

b. From the modeling and completion, is there any slack from each of these resources?
(Note: Slack is the remaining resource used, for example 200 tons are available but only 180 tons are used, so the slack from the equation is 20 tons)

2. If the Dava family wants to increase their resources, which resources need to be added? What is the highest cost that needs to be paid for the addition of these resources?
(You can get this from the sensitivity analysis of the resources used. The acquisition price for additional resources cannot be higher than the shadow price obtained)

3. If the Dava family had to choose between an additional 25000 tons of unpeeled durian and an additional 30 hours of oven roasting time, which one should the Agnis family take?


4. If the family plans to enlarge the oven at an additional cost of IDR 10,000,000 so they can bake 5 units of sponge cakes or 36 units of durian sus at once, should they enlarge the oven? Explain!

5. If the price of peeled durian rises to IDR 150,000 per pack, what will the Dava family do?

Answer rating: 100% (QA)

To solve this problem we can formulate a linear programming model to maximize the profit while considering the constraints and available resources Let... View the full answer