Question

The Versatech Corporation has decided to produce three new products. Five branch plants now have excess production capacity. The unit manufacturing cost of the first product would be $31, $29, $32, $28, and $29 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $45, $41, $46, $42, and $43 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $38, $35, and $40 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have the capability for producing this product. Sales forecasts indicate that 600, 1000, and 800 units of products 1, 2, and 3, respectively, should be produced per day. Plants 1, 2, 3, 4, and 5 have the capacity to produce 400, 600, 400, 600, and 1000 units daily, respectively, regardless of the product or combination of products involved. Assume that any plant having the capability and capacity to produce them can produce any combination of the products in any quantity

Answer 1

Answer: provided in the explanation segment

Step-by-step explanation:

here i will give a step by step analysis of the question;

A: Optimization Formulation

given Xij = X no. of units of product i manufactured in Plant j, where i = 1,2,3 and J = 1,2,3,4,5

Objective function: Minimize manufacturing cost (Z)

Z = 31 X11 + 29 X12 + 32X13 + 28X14 + 29 X15 + 45 X21 + 41 X22 + 46X23 + 42X24 + 43 X25 + 38 X31 + 35 X32 + 40X33

s.t

X11 + X12 + X13 + X14 + X15 = 600

X21 + X22 + X23 + X24 + X25 = 1000

X31 + X32 + X33 = 800

X11 + X21 + X31 <= 400

X12 + X22 + X32 <= 600

X13 + X23 + X33 <= 400

X14 + X24 ​​​​​​ <= 600

X15 + X25 <= 1000

Xij >= 0 for all i,j

B:

Yes, we can formulate this problem as a transportation problem because in transportation problem we need to match the supply of source to demand of destination. Here we can assume that the supply of source is nothing but the manufacturing capability of plant and demand of destination is similar to the demand of products.

cheers i hope this helps!!