8) A man owns two building supply stores, one on the east side and one on the west side of the city. Two customers order some inch plywood. Customer A needs 50 sheets and customer B needs 70 sheets. The east side store has 80 sheets and the west side store has 45 sheets of this plywood in stock. The east side store’s delivery costs per sheet are RM0.50 to customer A and RM0.60 to customer B. The west side store’s delivery costs per sheet RM0.40 to customer A and RM0.55 to customer B. How many sheets should be shipped from each store to each customer to minimize delivery costs?
Well, it's clear that we need to find the optimal allocation of plywood sheets from each store to each customer in order to minimize the delivery costs. Let's do some math (and clowning around) to figure it out!
Let's start with customer A. If we ship a sheet from the east side store, it will cost RM0.50, and if we ship it from the west side store, it will cost RM0.40. So, it's pretty obvious that we should ship all 50 sheets from the west side store for customer A. After all, why pay extra when you can get the same thing for less? It's like buying a brand-name cereal when there's a cheaper generic one right next to it. Don't fall for the fancy packaging, go for the deals!
Now, let's move on to customer B. If we ship a sheet from the east side store, it will cost RM0.60, and if we ship it from the west side store, it will cost RM0.55. Here, the difference is not as significant, but we should still be cost-conscious. With customer B needing 70 sheets, the east side store has enough to satisfy their demand, whereas the west side store falls short. So, we should allocate all 70 sheets from the east side store for customer B, as it will be cheaper than shipping them from the west side store. Plus, it's always nice to keep things balanced. East side, west side, everyone gets a little something!
So, to summarize: ship all 50 sheets for customer A from the west side store, and ship all 70 sheets for customer B from the east side store. This way, we minimize the delivery costs and keep everyone happy (and well-supplied with plywood).
Remember, my friend, always analyze the situation carefully before making decisions. Numbers don't lie, but they can be a bit tricky sometimes. Now, go out there and spread some cost-effective deliveries with a big ol' smile! 🤡
To minimize delivery costs, we need to calculate the number of sheets that should be shipped from each store to each customer. Let's assume that x sheets are shipped from the east side store to customer A, y sheets are shipped from the east side store to customer B, w sheets are shipped from the west side store to customer A, and z sheets are shipped from the west side store to customer B.
We can set up a system of equations based on the given information:
Equation 1: x + w = 50 (Total sheets ordered by customer A)
Equation 2: y + z = 70 (Total sheets ordered by customer B)
Equation 3: x + y ≤ 80 (Total sheets available at the east side store)
Equation 4: w + z ≤ 45 (Total sheets available at the west side store)
We also need to consider the delivery costs. The delivery cost from the east side store to customer A is RM0.50 per sheet, and to customer B is RM0.60 per sheet. The delivery cost from the west side store to customer A is RM0.40 per sheet, and to customer B is RM0.55 per sheet.
The total delivery cost can be calculated using the following equation:
Total delivery cost = (x * RM0.50) + (y * RM0.60) + (w * RM0.40) + (z * RM0.55)
To find the optimal delivery solution, we need to solve this system of equations and minimize the total delivery cost.
To minimize delivery costs, we need to determine the optimal number of sheets to be shipped from each store to each customer.
Let's assume that x represents the number of sheets shipped from the east side store to customer A, y represents the number of sheets shipped from the east side store to customer B, z represents the number of sheets shipped from the west side store to customer A, and w represents the number of sheets shipped from the west side store to customer B.
The objective is to minimize the total delivery cost, which can be calculated as follows:
Total Delivery Cost = (Number of sheets shipped from east side store to customer A * delivery cost per sheet from east side store to customer A)
+ (Number of sheets shipped from east side store to customer B * delivery cost per sheet from east side store to customer B)
+ (Number of sheets shipped from west side store to customer A * delivery cost per sheet from west side store to customer A)
+ (Number of sheets shipped from west side store to customer B * delivery cost per sheet from west side store to customer B)
Mathematically, the objective function can be expressed as follows:
Objective function = 0.5x + 0.6y + 0.4z + 0.55w
Subject to the following constraints:
1. x + z ≤ 80 (The total number of sheets shipped from both stores to customer A cannot exceed the stock of plywood at the east side store)
2. y + w ≤ 45 (The total number of sheets shipped from both stores to customer B cannot exceed the stock of plywood at the west side store)
3. x + y = 50 (Customer A needs 50 sheets)
4. z + w = 70 (Customer B needs 70 sheets)
Now, we need to solve this optimization problem using these constraints.
By solving these equations, we can find the optimal values of x, y, z, and w that minimize the delivery costs.