Marcy has $150 to buy packages of hot dogs and hamburgers for her booth at the carnival. At her local grocery store she found pa
ckages of hot cost $6 and packages of hamburgers cost $20. She has to use her entire budget of $150.
a. Solve the equation for b (burgers)
b. Solve the equation for d (hot dogs)
a. Solve the equation for b (burgers)
b. Solve the equation for d (hot dogs)
2 answers:
Total money that Marcy possess = $ 150
Cost of one hot dog= $ 6
Cost of one Hamburger = $ 20
If Marcy buys only Hamburger having cost b , then
b = = 7 Hamburger
If Marcy buys only Hotdogs having cost d , then
d =
And if Marcy buys both Hamburger and Hot dogs both, then
6 d + 20 b ≤ 150 ,b>0, d>0
3 d + 10 b≤ 75, b= Burger,→ X axis, d = Hot Dogs , →→Y axis
Plotting it on two dimensional plane
The positive integral value of x and y are the solution of the equation represented by : 3 y +10 x =75, for example y= 15 hamburger, and x =3 hot dog, is one solution of this line which is representation of burger and hot dog.
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Answer:
<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>
Step-by-step explanation:
Suppose, the number of Chef's salad is and the number of Caesar salad is
On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.
So, the two constraints are: and
The total number sold has never exceed 100 salads. So, another constraint will be:
According to the graph of the constraints, the vertices of the common shaded region are: and
<em>(Refer to the attached image for the graph)</em>
The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be:
For (40, 35) ,
For (60, 35) ,
For (60, 40) ,
For (50, 50) , <u><em>(Maximum)</em></u>
For (40, 50) ,
Profit will be maximum when and
Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.
