Question

A shop is selling stationery through two shops in town, and their website allows online orders. They receive online orders from two of their regular customers, each requiring glossy A3 printing paper. Customer X needs 40 boxes, whereas customer Y needs 60 boxes.

The shop in the north side of town has 85 boxes of glossy A3 paper in stock, whereas their south side shop has 55 boxes in stock. Delivery costs per box are as follows: $0.55 from the north shop to customer X, $0.65 from the north shop to customer Y, $0.45 from the south shop to customer X, and $0.60 from the south shop to customer Y.

Solve using simplex method and draw a clear graphical representation of the problem.

a) Develop the optimization problem to minimize the total delivery costs for this shop.

b) Identify how many boxes of glossy A3 paper need to be shipped from which shop to the two customers. Show your calculations in detail, along with a graphical interpretation of the problem and its solution.

Answer 1

Answer:

By using given data,

Let's use excel solver to solve this problem.

Since, Supply(140) and Demand(100) is not equal here, we will need to use a slack.

Let's fill in the values as below follows: -

Total Cost is the Σ cost/unit * optimum demand = sumproduct (cost*supplied value) as in cell C12

Now, the solver will find the optimum boxes in the second table. Keep the sum of Demands in this table as sum of demands fulfilled from North and South. Keep the sum of the Supply as the supply fulfilled for X and Y and Slack.

Configure the solver as below, objective is to minimize cost, by changing the cells in second table. The Constraints would be on the total supply and total demand.

Run the solver to get the below data -

(A)

Hence, the minimum delivery cost is $ 56.25

(B)

Customer X will be supplied 40 boxes from South side, Customer Y will be supplied 45 boxes from North side and 15 boxes from South side.