Assignment: Maximizing Income

A bakery makes Jumbo biscuits and Regular biscuits. The bakery is limited to:

a. The oven can bake at most 150 biscuits per day.
b. Each jumbo biscuit requires 2oz of flour and each regular biscuit requires 1oz of flour. The bakery has 200oz of flour available per day.
c. Due to cooking time constraints, the total number of regular biscuits cannot exceed 130
d. Due to cooking time constraints, the total number of jumbo biscuits cannot exceed 70.

The revenue from each jumbo biscuit sold is $1, and the revenue from each regular biscuit sold is $0.65. The cost to make each jumbo biscuit is $0.20, and the cost to make each regular biscuit is $0.15.

1. Let x be the number of Regular biscuits and y the number of Jumbo biscuits. Write an inequality for the limitations a, b, c, and d.

2. The bakery cannot produce less than zero of either type of biscuit either. Write an inequality for each type of biscuit that describes the minimum number of each type of biscuit.

3. Can the bakery produce 20 regular biscuits and 80 jumbo biscuits? If not, explain which limitations are violated.

4. Can the bakery produce 124 regular biscuits and 32 jumbo biscuits? If not, explain which limitations are violated.

5. Can the bakery produce 80 regular biscuits and 50 jumbo biscuits? If not, explain which limitations are violated.

6. Can the bakery produce 115 regular biscuits and 61 jumbo biscuits? If not, explain which limitations are violated.

7. Graph the system of 6 inequalities (from questions 1 and 2 above) and shade the area that shows the "feasible solutions", that is, the possible combinations of Regular and Jumbo biscuits.

The maximum and minimum profit will occur at one of the intersections bordering the feasible zone.

8. Find all the feasible intersections of limitations as ordered pairs.

9. Write an equation for the profit for the two types of biscuits and find the combination of Regular and Jumbo biscuits that produces the maximum profit.

a. Profit Equation:

b. Maximum Profit is: