local manufacturing firm produces four different metal products, each of which must be machined, polished, and assembled. The specific time requirements for each product are as follows:

Machining hoursPolishing hoursAssembling hoursUnit profit $Product 13126Product 22114Product 32226Product 44318

Every week, the firm has available to it a total of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time.

The firm has a contract with a distributor to provide 50 units of Product 1, and 100 units of any combination of Products 2 and 3 every week.

Through other customers, the firm can sell any number of units of Products 1, 2, and 3. However, no more than 25 units of Product 4 can be sold in a week.

How many units of each product should the firm produce each week, so that it can meet its contractual obligations, and maximize its total profit?

Fractional numbers are ok.

Every week, the firm has available to it a total of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time.

The firm has a contract with a distributor to provide 50 units of Product 1, and 100 units of any combination of Products 2 and 3 every week.

Through other customers, the firm can sell any number of units of Products 1, 2, and 3. However, no more than 25 units of Product 4 can be sold in a week.

How many units of each product should the firm produce each week, so that it can meet its contractual obligations, and maximize its total profit?

Fractional numbers are ok.

a. Production of Product 1 =

b. Production of Product 2 =

c. Production of Product 3 =

d. Production of Product 4 =

e. Total Profit = $

f. What should be the minimum unit profit (rounded to two decimal points) on Product 2, for the firm to be interested in producing it? Ans: $

g. The Operations Manager is thinking about increasing the capacity of polishing from 400 to 420 hours per week, at a very reasonable cost. Do you recommend the manager to go ahead with this proposal? Ans:

[ Select ]

["

Yes

", "

No

"]

h. The Sales team is working on renegotiating some of the constraints on minimum or maximum sales. They have three proposals.

(i) Proposal 1 is to reduce the contractual obligation for Product 1 from 50 units to 40 units.

(ii) Proposal 2 is to reduce the contractual obligation to make the sum of Product 2 and Product 3 from 100 units to 90 units.

(iii) Proposal 3 is to increase the maximum number of possible sales for Product 4 from 25 units to 35 units.

Based on your analysis, which of the proposals do you recommend the Sales team to implement? Ans:

[ Select ]

["

Proposal 1

", "

Proposal 3

", "

Proposal 2

"]