7. Two different resources (Workers X and Y) are engaged in the production of 4 products.  The next diagram specifies the required resources and rates of production. It also shows the raw material costs and product selling prices. The plant operates 24 hours a day (3 shifts), 5 days a week. There is only one Worker X and one Worker Y on each shift and they cannot substitute for each other.

At the given prices the market is willing to buy any quantity that the plant is able to produce, provided that the plant will offer the total spectrum of products. This constrains the product mix that can be sold, such that no single product can exceed the other by a factor of more than 5 (e.g. if Product A is to be sold in quantities of 1,000/day, the plant must produce at least 200/day of products B, C, and D as well). The total operating expenses of the plant – excluding the purchase of materials – are $8,000 per month (22 working days).

a)   What mix of the four products will you choose to offer the market?

Product	A	B	C	D
Ratio

 

b)  What is the profit associated with this mix?

c)   What production mix would you propose based on the “Goal”? (i.e. considering the theory of constraints, what mix will give highest profit?)

d)  How much additional profit would this optimal mix generate compared to b?