Question

A shop can sell at most 200 pairs of socks and at most 100 pairs of shoes. To maximize the profit, they have decided to make 2 offers. Offer 1 is a package of 1 pair of socks and 1 pair of shoes. Offer 2 is a package of 3 pairs of socks and 1 pair of shoes. The shop sells offer 1 for 30$ and offer 2 for 50$. They also want to sell at least 20 packages of offer 1 and at least 10 packages of offer 2. How many packages of each offer do they have to sell to maximize the profit

Answer 1

50 packages of offer 1 and 50 packages of offer 2

Step-by-step explanation:

Determine How many packages of each offer do they have to sell to maximize the profit

Number of package of offer 1 = x

Number of package of offer 2 = y

Applying the LPP model

max Z = 30 x + 50 y ---- ( 1 )

now subject to the constraints from Linear programming

x + 3y ≤ 200 ------ L1

x + y ≤ 100 ------ L2

x ≥ 20 ------------- L3

y ≥ 10 -------------- L4

therefore the number of packages of each offer that can be sold to maximize profit will be : X = 50 and Y = 50 referring to equation from the LPP model considering that the shop can sell at most 100 pairs