Problem

A company makes two types of biscuits: Jumbo and Regular. The oven can cook at most 300 biscuits per day. Each jumbo biscuit requires $2 \mathrm{oz}$ of flour, each regular biscuit requires $1 \mathrm{oz}$ of flour, and there is $400 \mathrm{oz}$ of flour available. The income from each jumbo biscuit is $\$ 0.07$ and from each regular biscuit is $\$ 0.13$. How many of each size biscuit should be made to maximize income? What is the maximum income? The company should make jumbo and regular biscuits. (Type whole numbers.) The maximum income is $\$ \square$. (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Step 1 :This problem is a linear programming problem. The goal is to maximize the income from selling biscuits, subject to the constraints of the oven capacity and the available flour.

Step 2 :The constraints can be represented as follows: The total number of biscuits (jumbo and regular) should not exceed 300. The total amount of flour used (2 oz for each jumbo and 1 oz for each regular biscuit) should not exceed 400 oz.

Step 3 :The objective function (income) to be maximized is \(0.07 \times \text{number of jumbo biscuits} + 0.13 \times \text{number of regular biscuits}\).

Step 4 :By solving this linear programming problem, we find that the optimal solution is to make 0 jumbo biscuits and 300 regular biscuits.

Step 5 :The maximum income from selling these biscuits is \(\boxed{39.00}\).

From Solvely APP
Source: https://solvelyapp.com/problems/12538/

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