15 An appliance store sells two brands of televisions. Each Daybrite set sells for $425, and each Noglare set sells for $700. The store’s warehouse capacity for television sets is $400, and new sets are delivered only each month. Records show that customers will buy at least 70 Daybrite sets and at least 160 Noglare sets each month. How many of each brand should the store stock and sell each month to maximize revenue?

The store should stock and sell _ Daybrite sets and _ Noglare sets.

If there are x Daybrite sets and y Noglare sets, then you want to

maximize p=425x+700y subject to
x+y <= 400
x >= 70
y >= 160

a good tool is at

http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html

it will solve and graph the solution

To maximize revenue, we need to determine the number of Daybrite sets and Noglare sets the store should stock and sell each month.

Let's assume the store stocks and sells x units of Daybrite sets and y units of Noglare sets.

Given:
- Each Daybrite set sells for $425, and each Noglare set sells for $700.
- The store's warehouse capacity for television sets is 400 units.
- Records show that customers will buy at least 70 Daybrite sets and at least 160 Noglare sets each month.

To maximize revenue, we need to set up an objective function based on the number of units sold and the selling prices.

Objective function:
Revenue = 425x + 700y

We also have some constraints:
1. Warehouse capacity: x + y ≤ 400
2. Minimum number of Daybrite sets sold: x ≥ 70
3. Minimum number of Noglare sets sold: y ≥ 160

Now, let's solve this problem using linear programming:

Step 1: Optimize the objective function subject to the given constraints.

Step 2: Solve the system of inequalities to find the feasible region.

x + y ≤ 400
x ≥ 70
y ≥ 160

The feasible region is the intersection of these inequalities.

Step 3: Substitute the corner points of the feasible region into the objective function.

The corner points of the feasible region will be the vertices of the polygon formed by the intersection of the inequalities.

Using these corner points, calculate the revenue for each combination of x and y values:

Corner Point 1: (70, 160)
Revenue = 425(70) + 700(160) = $203,000

Corner Point 2: (70, 400)
Revenue = 425(70) + 700(400) = $394,500

Corner Point 3: (230, 160)
Revenue = 425(230) + 700(160) = $214,250

Corner Point 4: (230, 230)
Revenue = 425(230) + 700(230) = $345,500

Corner Point 5: (230, 400)
Revenue = 425(230) + 700(400) = $534,250

Corner Point 6: (400, 160)
Revenue = 425(400) + 700(160) = $324,000

Corner Point 7: (400, 400)
Revenue = 425(400) + 700(400) = $660,000

Step 4: Compare the revenues and find the combination that gives the maximum revenue.

From the calculations, we can see that the maximum revenue is obtained at Corner Point 7: (400, 400). This means the store should stock and sell 400 Daybrite sets and 400 Noglare sets each month to maximize revenue.

Therefore, the store should stock and sell 400 Daybrite sets and 400 Noglare sets each month to maximize revenue.