I need help coming up with the formulas to show the highest profit from the foll

Question

I need help coming up with the formulas to show the highest profit from the following table in excel. There is also the following criteria.

The nails will be sold in boxes of up to 30 nails.

There must be no more than 10, but no less than 5, of each of three types of nails in each box. Note: There must be three types of nails per box – no more, no less.

The nails in each box should weigh no more than 20 ounces.

Nail Weight Cost Selling Price
4 inch 1 oz 4 cents 8 cents
3.5 inch 0.85 oz 3.5 cent 6 cents
3 inch 0.7 oz 3 cents 5 cents
2.5 inch 0.5 oz 2.5 cents 4 cents
2 inch 0.25 oz 2 cents 3 cents
1.5 inch 0.1 oz 1.5 cents 2 cents

Explanation / Answer

Hey, Running this through excel you get the profit maximization of: 10 5 5 0 9 0 10 9 0 0 9 0 10 10 0 0 4 5 10 6 0 5 9 0 This is listed in the order of nails 4 to 1.5. For example the first row shows a profit maximization if the box contains 10 of the 4 inc nails, 5 of the 3.5 inch nails, 5 of the 3inch nails....etc. All of these rows yield a profit of 71.5 cents I used the objective function in excel of z=4x_1 + 2.5x_2 +2x_3 + 1.5x_4 + x_5 +.5x_6 and added in the parameters that you indicated in the problem.

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