A company is producing two types of storage cabinets, "Brown" and "Black". The time requirements for each stage of production and the labour-hours available for each stage are given in the following table. The table also shows the unit profit of each type of cabinet.

Product

Stage I (Assembling)

Stage II (Finishing)

Unit profit

Brown

4

10

$150

Black

8

6

$200

Max available time (hrs/week)

100

110

PARTA.Determine how many storage cabinets per week of each type must be produced to maximize the total profit. (Fractional units allowed).

1. Number of "Brown" cabinets?

1. Number of "Black" cabinets?

1. Maximumprofit?

PARTB.Suppose that a single order is received for 8 "Brown" cabinets, and if it is decided that this ordermustbe filled, determine the new values below (fractional units allowed)):-

1. Number of "Brown" cabinets?

1. Number of "Black" cabinets?

• Maximum profit?

PARTC.Now, in addition to the above, make allowance for an extra market constraint that the demand for the two types of cabinets is no more than12per week in total.Again determine how many cabinets of each must be produced to maximize the total profit (fractional units allowed):-

1. Number of "Brown" cabinets?

1. Number of "Black" cabinets?

1. Maximum profit?

• What happens to the maximum profit after each extra constraint is added?

11.Why does this happen?