To attract customers during the first weeks of its operation, your company will

Question

To attract customers during the first weeks of its operation, your company will run a special promotion. Three burgers will be specially priced to compete favorably against the best-selling burger of each of your 3 competitors. Your resaurant's Super Lean Burger uses .2 lb of beef and .03 lb of seasoning mix. It will be priced at a loss of $.12 per burger. The deluxe Stuffed Burger uses .23 lb of beef and .1 lb of mix. It will be sold at a loss of $.08. Finally, Super-Duper Deluxe Burger uses .3 lb and .01 lb of mix. Your company will lose $.05 on each burger of this type sold. Your restaurant's chef has ordered and allocated 3000 lb of beef and 400 lb of seasoning mix for making the burgers during this promotion. Your company's accountant has set a limit of $1000 loss for this promotion.

Determine the number of each type of burger your restaurant should plan to sell during this promotion.

Explanation / Answer

Let the Super Lean Burger be represented by L, the deluxe Stuffed Burger by S, an the Super-Duper Deluxe Burger by D. So for the equation with the beef, we get:

0.2L + 0.23S + 0.3D = 3000

For the mix, we get:

0.03L + 0.1S + 0.01D = 400

For the loss, we get:

0.12L + 0.08S + 0.05D = 1000

So then we can start by multiplying the second equation by 4, and then subtracting the third equation from that:

0.32S - 0.01D = 600

Then we multiply the first equation by 3 and the last equation by 5 and subtract them to get:

0.29S + 0.65D = 4000

Then we multiply that above equation by 65 and then add to get:

21.09S = 43000

S = 2039.

We plug that back in to get:

D = 5244

and finally, we substitute back in to get:

L = 4789

So they should sell 4789 Super Lean Burgers, 2039 deluxe Stuffed Burgers, and 5244 Super-Duper Deluxe Burgers.

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